A Complete Bibliography of the LAPACK Working Notes

Nelson H. F. Beebe University of Utah Department of Mathematics, 110 LCB 155 S 1400 E RM 233 Salt Lake City, UT 84112-0090 USA

Tel: +1 801 581 5254 FAX: +1 801 581 4148

       E-mail: beebe@math.utah.edu, beebe@acm.org,
                  beebe@computer.org (Internet)
      WWW URL: http://www.math.utah.edu/~beebe/

01 March 2018 Version 2.24

Title word cross-reference

(A, B) [333]. 1 [152]. 2.5 [237, 247]. AX − XB = C [42, 312]. dqds [358, 155]. LU [80, 357, 40, 204, 67, 110, 118, 338, 258, 271, 281, 226, 262, 265, 237, 247, 202]. QR [233, 224, 241, 122, 31, 294, 239, 276, 8, 286, 190, 368, 187, 80, 329, 357, 15, 45, 299, 204, 203, 275, 118, 256, 176, 251, 271, 281, 216, 222, 79, 332, 121, 363, 270, 201, 229, 114, 240, 202]. QZ [173].

-590 [71]. -Norm [152].

/ [380, 374].

1.0 [98]. 1.1 [137]. 1.2 [140, 102]. 11th [375]. 14th [372]. 1990 [370]. 1994 [378]. 1997 [385]. 1998 [384].

2.5 [174]. 2005 [164]. 2nd [377].

3 [185, 114].

590 [71].

64-bit [180]. 679 [290]. 680 [266]. 6th [376].

754 [172].

’90 [371, 158, 117, 101, 331]. 90-enhanced [158]. 90-VAPP [370]. ’92 [374]. ’95 [382]. ’96 [381].

Accelerate [197]. Accelerated [259, 210]. Accelerating [245, 219]. acceleration [156]. Accelerators [233, 223, 225]. Access [6, 285]. Accuracy [180, 3, 119, 183, 258, 175, 352]. Accurate [7, 289, 15, 48, 299, 307, 130, 169, 170]. Achieving [180, 258]. ACM [384]. ACM/IEEE [384]. Across [73]. Acyclic [48, 307]. Adapting [160, 365, 157]. Aggregated [253]. Aggressive [187, 173]. Ahead [178]. Aid [6, 285]. Algebra [230, 20, 288, 26, 44, 200, 106, 320, 218, 328, 263, 191, 274, 160, 55, 92, 100, 95, 330, 1, 47, 60, 309, 164, 186, 290, 28, 293, 37, 43, 58, 61, 311, 98, 99, 346, 50, 77, 242, 178, 213, 250, 139, 356, 359, 221, 210, 225, 134, 73, 131, 349, 304, 296, 313, 321, 367, 301, 234, 254]. Algebraic [79, 332]. Algorithm [122, 19, 168, 38, 68, 187, 152, 129, 56, 124, 351, 162, 169, 170, 252, 199, 282, 52, 323, 79, 332, 121, 363, 173, 167, 163, 90, 324, 69, 132, 197, 195, 276, 343, 159, 273, 216, 226, 211, 358, 155, 342, 290, 96]. Algorithm-Based [90, 324, 252]. Algorithmic [76, 326, 205, 279, 128, 133, 355]. Algorithms [191, 65, 125, 22, 300, 59, 317, 322, 24, 248, 242, 87, 75, 198, 171, 214, 208, 246, 250, 243, 113, 115, 221, 314, 256, 333, 334, 270, 237, 247, 57, 315]. Algorithms-By-Tiles [208, 214]. Analysis [6, 242, 115, 73, 285, 372, 312]. Annual [377]. ANSI [111]. Application [179]. Applications [31, 157, 365, 88, 294, 385]. Applied [205, 383, 382]. Approach [76, 263, 103, 353, 326]. April [377, 373]. Architecture [266]. Architectures [241, 200, 191, 190, 368, 30, 61, 74, 318, 222, 242, 121, 363, 278, 214, 208, 209, 246, 250, 243, 249, 132, 73, 260, 238, 303]. Arithmetic [322, 175, 375]. Array [120, 344, 345]. Assessing [268]. Asynchronous [257, 259, 124, 351]. ATLAS [349, 147, 361]. August [382, 383]. Auto [212]. Auto-tuning [212]. Automated [147, 361]. Automatic [151]. Automatically [131, 349]. Autotuned [241]. Autotuning [244, 266]. Avoid [284]. Avoiding [239, 275, 240, 262]. Aware [253, 254].

B [87]. backends [283]. Backward [42, 312]. Band [21, 209]. Banded [142, 143, 350, 125, 12]. Based [205, 107, 108, 90, 324, 252, 278, 219, 347].

Basic [100, 330, 37, 311, 77, 73, 156, 290]. been [116]. Benchmark [206, 107, 108, 177, 347]. Benefits [97, 172]. Better [230]. Between [75, 334]. BiCGstab [78]. Bidiagonal [92, 11, 292, 3, 246, 166, 313, 321]. Bidiagonalization [174, 209]. Bisection [70, 322, 197]. Bisection-Like [322]. bit [180, 175]. BLACS [34, 94]. BLAS [21, 316, 22, 300, 109, 291, 174, 107, 108, 347, 283, 149, 364, 12, 114]. BLAS-3 [114]. Block [19, 257, 8, 286, 68, 152, 316, 22, 40, 300, 120, 344, 345, 2, 287, 24, 171, 208, 128, 133, 355, 113, 196]. Block-Asynchronous [257]. Block-Cyclic [120, 344, 345, 355]. Block-Partitioned [113]. Blocked [198]. Blocks [54, 306, 151]. Bombardment [76, 326]. Bonn [385]. Bounds [23, 308, 165, 83, 238, 341]. Bulge [187]. bulges [270]. Butterfly [284].

C [111, 74, 318]. Cache [174]. California [380]. Call [82]. CALU [226]. Can [163]. Capabilities [202]. Capability [271]. Cartesian [52, 323]. case [176, 358, 155]. CCI [82]. CELL [189, 177, 184, 201]. Center [384, 371]. CGS [78]. chains [270]. Characterization [66]. Cheaper [230]. Checkpointing [277, 280, 268, 90, 324, 267, 273]. chemistry [382]. choice [159]. Cholesky [146, 360, 215, 80, 329, 357, 14, 118, 211, 199, 248, 184, 223, 161, 12, 202]. Class [191]. clMAGMA [274]. Cluster [185, 240, 256]. Clusters [160, 163, 276]. CMake [269]. Codes [161]. Coding [111]. Collection [123]. collectives [254]. Column [275, 114]. Combination [277]. Combine [29, 319]. Combining [267]. Communication [239, 215, 218, 236, 238, 56, 204, 275, 37, 311, 99, 237, 247, 240, 73, 226, 262, 254]. Communication-Avoiding [239, 240]. Communication-optimal [215, 204, 237, 247]. Comparative [217]. Comparison [142, 143, 350, 279]. Complex [153]. Complexity [67]. Components [193]. componentwise [207]. Computation [88, 72, 335, 374, 272, 383]. Computational [78]. Computations [180, 164, 2, 167, 249, 287, 382]. Computer [58, 375]. Computers [20, 288, 26, 91, 336, 328, 55, 65, 57, 95, 129, 1, 86, 164, 127, 296, 314, 315, 343]. Computing [384, 224, 193, 38, 46, 305, 7, 289, 148, 112, 337, 205, 185, 3, 48, 307, 119, 352, 25, 302, 378, 373, 380, 87, 333, 220, 359, 376, 166, 362, 327, 231, 385, 382, 219, 383]. Concepts [110, 77, 338]. Concurrent [55, 65, 57, 129, 296, 314, 315, 343]. Condensed [2, 30, 253, 287, 303]. Condition [32, 33, 4, 87, 207, 272, 295, 333]. Conditioning [193, 13, 235]. Conference [381, 384, 370, 372, 373, 379, 376, 377]. Conjugate [56, 51, 159]. CONPAR [370]. Conquer [125, 69, 132]. Considerations [25, 302]. Contents [5]. contribution [235]. Convention [384]. convergence [196]. Conversion [82]. Core [217, 110, 178, 357, 118, 338, 256, 249]. Correction [259]. Correctness [70, 322]. Costs [56]. County [384]. CPU [265]. CPUs [229]. Cray [126]. Criterion [122]. CUDA [228]. Cuppen [69]. Cyclic [120, 344, 345, 128, 133, 355, 196].

D [237, 247]. DAG [231, 263]. DAGuE [231, 232]. Dangers [112, 337, 327]. Data [97, 50]. Decomposition [239, 46, 91, 336, 236, 11, 292, 119, 88, 115, 305, 215, 352]. Decompositions [128, 355]. Deflation [122, 187, 173]. Denmark [382, 383]. Dense [241, 200, 263, 274, 92, 86, 43, 252, 242, 250, 243, 210, 225, 179, 260, 313, 321, 301, 234, 254]. Dependence [232]. derive [207]. Design [328, 137, 140, 80, 92, 95, 329, 4, 162, 58, 61, 118, 149, 364, 313, 321, 357]. Designer [139, 356, 359]. Designing [39, 298, 281]. Detection [277]. Determination [151]. Develop [230]. Development [1]. Diagonal [54, 306, 105, 340]. Diagonally [142, 143, 350, 7, 289]. Diagonals [203]. Digest [380]. Dimensional [37, 311]. Direct [284, 38]. directions [385]. Discontinuous [150]. Diskless [90, 324]. Dissection [52, 323]. Distributed [91, 336, 328, 232, 263, 55, 65, 57, 95, 129, 56, 86, 30, 61, 50, 77, 62, 121, 363, 359, 64, 325, 221, 132, 231, 296, 314, 315, 343, 303, 216]. Distributed-Memory [232, 129, 221, 343]. Distributions [133, 116]. Divide [125, 69, 132]. Divide-and-Conquer [125]. DoD [136]. doing [116]. Dominant [142, 143, 350, 7, 289]. double [273]. DPLASMA [232]. dual [207]. Dundee [372]. Dynamic [220, 221]. Dynamically [242].

Early [187, 173]. Efficiency [250]. Efficient [272, 67, 88, 174, 249]. Efficiently [89, 148, 362]. Eigenproblem [13, 17]. Eigenproblems [236]. Eigenroutines [4]. Eigensolvers [183, 182, 172]. Eigenspace [85, 354]. Eigenspaces [87, 333]. Eigensystems [7, 289]. Eigenvalue [150, 168, 123, 322, 2, 30, 153, 253, 79, 332, 84, 348, 163, 115, 69, 132, 287, 303, 192]. Eigenvalues [38, 48, 307, 86, 87, 197, 333]. Eigenvector [153]. Eigenvectors [86, 154, 366]. Elementary [72, 335]. Elimination [124, 351, 279, 127, 64, 325]. Empirical [241, 147, 361]. enables [269]. End [164]. Energy [280, 250]. engine [231]. engineering [382]. Enhance [180]. Enhanced [233, 158]. Enhancing [222]. Environment [224, 139, 356, 359]. Environments [378]. Equation [75, 334]. Equations [184, 89]. Error [259, 277, 23, 308, 165, 251, 42, 278, 115, 312]. Errors [14, 255]. ESSL [71]. estimates [272]. Estimating [75, 334]. Estimation [32, 33, 152, 4, 87, 295, 333]. Evaluating [19]. Evaluation [136, 107, 108, 347]. Exascale [267, 261, 264]. Exception [59, 317]. exchangeable [283]. Execution [232, 234]. Existence [144]. Experience [112, 337, 327]. Experiments [17]. Exploiting [291, 175]. Extended [149, 364]. Extension [26]. Extensions [135]. Extra [165, 188, 369]. Extra-Precise [369, 188]. Extreme [268]. Extreme-Scale [268].

Factor [83, 341]. Factorisation [144, 145]. Factorization [233, 224, 241, 31, 190, 368, 80, 40, 275, 67, 24, 110, 118, 258, 251, 199, 248, 222, 184, 201, 229, 265, 223, 114, 64, 240, 146, 360, 294, 276, 329, 357, 338, 256, 176, 226, 262, 12, 325, 237, 247]. Factorizations [217, 21, 252, 161, 202, 204]. Fail [163]. failure [176]. Fast [189, 22, 300, 186, 367, 169, 170, 291]. Faster [230, 59, 317]. Fault [205, 252, 380, 90, 324]. Fault-Tolerant [380, 324]. Features [172]. Fermi [244, 227]. fifth [380]. Finding [86, 197]. Fine [253]. Fine-Grained [253]. Finite [159]. Finite-choice [159]. FlexiBLAS [283]. flexible [283]. Floating [14, 49, 70, 322, 175]. Florida [384]. Form [54, 306, 68, 92, 30, 198, 313, 321, 303, 219]. Format [199, 211]. Forms [2, 253, 171, 287, 192]. formulation [146, 360]. FORTRAN [6, 285, 158, 117, 101, 331]. Fourth [374]. Framework [271, 51]. Frontiers [374]. Full [199]. Fully [241, 220, 211]. functional [207]. fundamentals [385].

Gaps [154, 366]. Gaussian [124, 351, 279, 127, 64, 325]. GeForce [266]. GEMM [107, 108, 347, 266, 212, 227]. GEMM-based [347, 107, 108]. GEMMs [244]. General [142, 143, 350]. Generalized [31, 294, 46, 32, 75, 171, 305, 334]. Generalizing [295]. Generation [9, 157, 365]. Generator [206]. generic [231]. geodesy [179]. Germany [385]. Givens [148, 362]. Global [29, 319, 196]. GPU [233, 259, 228, 271, 278, 229, 265, 223, 249, 210, 219, 225]. GPU-Accelerated [259]. GPU-based [278, 219]. GPUs [230, 239, 212, 227, 202, 197]. Gradient [56, 51]. Gradients [159]. Grained [253]. Graphics [257]. Graphs [48, 307]. Grid [224, 156]. group [264]. GTX [266]. Guaranteed [3]. Guide [18, 41, 81, 137, 93, 102, 98, 94, 35]. Guidelines [4].

Hamiltonian [11, 292]. Handling [59, 317]. Hardware [217, 263, 282]. held [385]. Hermitian [123]. Hessenberg [8, 286, 68, 313, 92, 321, 278, 198, 208, 219]. Hessenberg-Triangular [198]. Heterogeneous [112, 337, 263, 249, 238, 327]. Hierarchical [256]. High [384, 20, 288, 26, 111, 205, 185, 274, 1, 3, 39, 298, 119, 164, 203, 58, 61, 74, 318, 98, 346, 258, 255, 211, 373, 107, 177, 127, 223, 246, 250, 134, 231, 352, 347]. High-Performance [20, 288, 26, 111, 1, 107, 347]. Highly [68]. Hilton [371]. Homogeneous [246]. Householder [203]. HPC [216]. HPF [137]. Hybrid [251, 278, 210, 281, 216, 211, 219]. Hybridization [230].

IBM [28, 293, 71]. IEEE [172]. IEEE-754 [172]. II [143, 170, 85, 354]. IML [102]. Implementation [18, 35, 8, 286, 187, 140, 152, 80, 125, 316, 162, 290, 118, 282, 121, 363, 177, 229, 149, 115, 69, 73, 329, 357, 364, 358, 155]. Implementations [279, 107, 108, 347]. Implementing [276, 178]. Implicit [45]. Improved [23, 308, 282, 227]. Improvements [126]. Improving [254]. Inaccuracy [45]. Incomplete [144, 145]. Incremental [32, 33, 179, 295]. indefinite [260]. industrial [383]. industrial-strength [383]. Infrastructure [182]. Inherent [45]. Initial [10, 16]. Installation [41, 81, 137, 93, 108]. Installing [10]. Intel [24]. Interface [117, 82, 101, 99, 137, 331]. International [370, 380, 383, 382]. Invariant [38, 25, 302]. Inversion [297, 27, 199]. iPSC [24]. iPSC/860 [24]. Issues [200, 328, 95]. Iteration [8, 286]. Iterative [259, 76, 4, 165, 188, 369, 102, 99, 66, 141, 104, 339, 175, 326]. IV [370].

Jacobi [15, 299, 169, 170, 196]. Joint [370]. July [375]. June [372, 380, 375].

Kepler [266]. kernel [211]. Kernels [189, 253, 266]. Key [110, 338].

Lanczos [51]. LAPACK [10, 16, 19, 18, 20, 288, 26, 35, 44, 304, 126, 158, 41, 81, 117, 187, 160, 152, 164, 183, 181, 182, 24, 82, 98, 101, 331, 104, 339, 75, 334, 269, 161]. LAPACK-style [334, 75, 161]. LAPACK/ESSL [82]. LAPACK3E [158]. LAPACK90 [346, 138, 134]. LAPACKE [269]. Least [193, 188, 369, 88, 113, 179, 207, 235, 272]. Level [21, 316, 22, 300, 290, 211, 248, 291, 107, 108, 161, 347, 12]. Level-3 [316, 300, 211, 248]. Libraries [39, 298, 181, 43, 58, 379, 301]. Library [20, 288, 26, 44, 328, 92, 95, 1, 74, 318, 102, 304, 296, 313, 321, 283, 269, 126]. Like [322]. Limitations [185]. Line [63]. Linear [230, 20, 288, 26, 44, 142, 143, 350, 193, 200, 106, 320, 218, 76, 328, 263, 191, 274, 160, 55, 92, 100, 95, 330, 125, 1, 4, 47, 60, 309, 164, 186, 290, 28, 293, 37, 43, 58, 61, 311, 98, 99, 346, 255, 50, 77, 141, 242, 62, 178, 184, 213, 175, 250, 139, 356, 359, 113, 221, 210, 225, 134, 73, 131, 349, 304, 207, 245, 272, 326, 296, 313, 321, 367, 301, 234, 339, 254]. LINPACK [177, 206]. Look [43, 178, 301]. Low [203]. Low-Profile [203]. LU [329]. Lyngby [382, 383].

MAGMA [227]. Many [248]. Manycore [210]. Massively [374]. Matrices [224, 91, 336, 7, 289, 21, 3, 48, 307, 86, 130, 203, 2, 72, 335, 243, 197, 287]. Matrix [189, 123, 68, 111, 180, 152, 65, 57, 315, 129, 297, 9, 74, 318, 206, 252, 27, 51, 151, 291, 87, 75, 209, 90, 324, 116, 249, 96, 146, 360, 314, 343, 333, 334, 237, 247, 342]. Matrix-Blocks [151]. May [378]. McLean [374]. Mechanics [11, 292]. Memory [91, 336, 328, 232, 6, 55, 65, 57, 95, 129, 56, 86, 30, 61, 253, 121, 363, 265, 221, 132, 285, 296, 314, 315, 343, 303, 216]. Memory-Aware [253]. Method [257, 15, 299, 105, 340, 145]. Methodology [230, 111]. Methods [284, 297, 102, 99, 27, 51, 66, 144, 17, 128, 133, 355, 196, 78]. Microsoft [269]. MIMD [316]. minimal [211]. Minimizing [218, 236]. Mississippi [379]. Mixed [259, 180, 97, 177, 149, 207, 364]. Mixed-Precision [177]. Model [268, 290, 107, 108, 347]. Modeling [97]. modelling [234]. Modern [172]. modification [145]. MRRR [168, 162, 167, 163, 194, 195]. MSRCs [136]. Multi [217, 187, 228, 178, 265, 249, 256, 156]. Multi-Core [217, 178, 249, 256]. Multi-CPU [265]. Multi-GPU [265, 249]. multi-grid [156]. Multi-platform [228]. Multi-shift [187]. Multicore [233, 241, 200, 191, 190, 368, 222, 242, 282, 220, 213, 214, 208, 209, 223, 246, 250, 243, 221, 240, 225, 276, 260]. Multiple [217, 233, 255, 229, 73, 166]. Multiplication [189, 57, 315, 129, 291, 96, 343, 237, 247, 342]. Multiply [111]. Multiprocessor [67]. Multiprocessors [56]. Multishift [8, 286, 173, 270]. Myths [79, 332].

Narrow [142, 143, 350]. Narrow-Banded [142, 143, 350]. Negative [203]. Nested [52, 323]. NetSolve [140]. Networking [384]. Next [181, 157, 365]. Node [233]. Non [10, 123, 203]. Non-Hermitian [123]. Non-Negative [203]. Non-Unix [10]. Nonsymmetric [13, 91, 336, 68, 121, 363]. Norfolk [376]. Norm [152]. Note [212]. Notes [187]. novel [216]. November [381, 384, 371]. numbers [207]. Numerical [44, 337, 160, 39, 298, 47, 53, 59, 60, 309, 310, 317, 279, 25, 302, 157, 365, 258, 372, 220, 139, 356, 359, 304]. numerics [377]. NVIDIA [266].

Object [61, 377]. Obtaining [175]. October [379, 374]. Off [53, 310]. One [217]. One-Sided [217]. Ontario [375]. Open [47]. OpenCL [274, 228]. Operations [28, 293, 50, 77, 213, 90, 324, 29, 319]. Operators [174]. Optimal [280, 215, 204, 226, 237, 247]. Optimally [270]. optimised [156]. Optimization [147, 159, 383]. optimizations [361]. Optimizing [111]. Orange [384]. Oriented [61, 377]. Orlando [384]. Orthogonal [154, 366, 64, 325]. Out-Of-Core [110, 118, 357, 338]. Overdetermined [188, 369]. Overlap [67]. Overview [141].

PA [381]. Package [346, 134]. Packages [217, 141]. Packed [135, 199, 146, 360, 270]. Pair [87, 333]. Pairs [75, 334]. panel [262]. Papers [385, 380]. PARA [382, 383]. Parallel [168, 142, 143, 350, 179, 91, 336, 215, 68, 370, 191, 190, 368, 65, 314, 92, 100, 129, 316, 49, 60, 309, 70, 322, 124, 351, 279, 378, 110, 118, 153, 192, 253, 282, 52, 323, 121, 363, 379, 208, 209, 359, 116, 374, 376, 73, 260, 313, 321, 343, 357, 204, 382, 338, 234, 216, 237, 247, 383, 57, 315, 330, 385]. Parallelism [97, 53, 310, 222]. Parallelizing [79, 332, 132]. ParCo97 [385]. PaRSEC [276]. Part [248]. Partial [103, 353, 105, 340, 265, 234]. Partitioned [113]. Pasadena [380]. Patterns [6, 285]. PDSYEVR [168]. 6000 [28, 293]. 6000-550 [71]. 860 [24]. ESSL [82]. IEEE [384]. QL [17]. Performance [384, 20, 288, 26, 44, 304, 126, 111, 328, 136, 205, 180, 185, 274, 95, 1, 39, 298, 86, 183, 203, 67, 279, 58, 61, 71, 74, 318, 98, 346, 258, 228, 255, 211, 373, 107, 108, 177, 175, 127, 246, 250, 134, 231, 234, 281, 347, 254]. Performance-portable [228]. Performant [223]. Period [280]. Perspective [139, 356, 359]. Perturbation [42, 312, 83, 84, 85, 348, 354, 341]. PHiPAC [111]. physics [382]. Pipelining [67, 178]. Pittsburgh [381]. Pivoted [161]. Pivoting [284, 103, 353, 275, 105, 340, 265, 114, 262]. Plane [150, 63]. platform [228]. PlayStation [185]. Point [14, 49, 70, 322, 175]. Polar [83, 341]. Poly [76, 326]. Poly-Iterative [76, 326]. Polynomial [66, 156]. Portable [20, 288, 26, 44, 111, 328, 95, 39, 298, 304, 228, 211]. positive [358, 155]. Power [250]. Practical [112, 327, 337]. Precise [165, 369, 188]. Precision [259, 180, 177, 149, 364]. Prefix [49]. Preliminary [266]. Problem [150, 168, 30, 206, 144, 79, 332, 139, 356, 359, 113, 69, 132, 235, 303]. Problems [106, 320, 123, 47, 188, 369, 88, 253, 179, 272]. Proceedings [381, 384, 371, 379, 375, 370, 372, 383, 378, 382]. Process [267]. Processing [257, 370, 376]. Processor [189, 184, 201, 177]. Processors [316, 178, 220, 213]. Profile [203]. Profiling [250]. Programming [228]. Programs [6, 290, 285]. project [361, 232, 147]. proof [196]. Properties [279, 51]. Proposal [100, 101, 330, 331]. Prospectus [26, 1, 164, 181]. Protocols [268]. Providing [271]. Provisional [5]. PUMMA [57, 315]. Purpose [200].

QR [17]. QR/QL [17]. Qualitative [51]. Quick [81].

Random [284]. randomization [245]. Rank [275, 176, 262]. Real [54, 306, 192]. Reality [79, 332]. Rectangular [199]. Recursive [258, 146, 360]. Redistribution [120, 344, 345, 128, 133, 355]. Reducing [56, 234]. Reduction [68, 92, 2, 30, 303, 253, 278, 198, 208, 246, 243, 313, 321, 287, 219]. Reference [102]. Refined [194]. Refinement [259, 4, 165, 188, 369, 104, 175, 339]. Regular [87, 75, 333, 334]. Relative [3, 119, 154, 366, 83, 84, 85, 341, 348, 354, 352]. Relatively [166]. Relaxation [257]. Release [10, 16]. Reliable [164]. reliably [148, 362]. Reordering [171, 192]. Replication [267, 261, 264]. Representation [194]. Representations [166]. Resilience [255, 267, 261, 264]. Resilient [251, 278]. Results [16, 266]. Revealing [275, 176, 262]. Reverse [99]. Revisited [198, 208]. Revisiting [273, 175]. right [116]. RISC [28, 293]. Robust [36, 33, 166]. Rockefeller [371]. Rotations [150, 148, 362, 196]. Routines [44, 80, 71, 118, 153, 248, 178, 304, 329, 357, 234]. RS [71]. RS/ 6000 [71]. RS/6000-550 [71]. runtime [283].

SC98 [384, 384]. Scalable [55, 164, 43, 373, 379, 223, 240, 296, 301, 342, 96]. ScaLAPACK [168, 328, 137, 136, 55, 296, 80, 95, 329, 93, 125, 135, 357, 181, 118, 271, 195]. Scale [268]. Scaled [7, 289]. Scheduled [242]. Scheduler [220]. Scheduling [120, 344, 345, 213, 214, 221]. Schur [54, 306, 192, 171]. science [382]. Scientific [126, 378, 359, 376]. Second [378, 382]. Secular [89]. Selected [71]. Self [160, 157, 365]. Self-Adapting [365, 157]. Separating [75]. separation [334]. Separators [63]. Sept [385]. September [370]. Sequential [215, 204]. Serial [69]. Set [100, 290, 330]. Shared [265]. shift [187]. Short [189]. SHPCC [373]. SHPCC-92 [373]. SIAM [376]. Sided [217, 209, 214]. Silent [277]. SIMD [189]. Singular [46, 236, 11, 292, 3, 48, 307, 119, 88, 282, 348, 354, 115, 305, 352]. Skinny [224]. SLHPF [137]. Small [189, 187, 3]. smoothers [156]. Soft [255, 251]. Software [217, 230, 13, 160, 92, 164, 138, 157, 365, 87, 75, 131, 147, 313, 321, 176, 333, 334, 361, 349]. Solution [193, 76, 228, 199, 62, 207, 326]. solutions [245]. Solver [255, 141, 260]. Solvers [142, 143, 350, 23, 308, 225, 36, 281]. Solving [75, 184, 89, 139, 356, 359, 113, 179, 334]. Some [200, 322, 115]. space [179]. Sparse [284, 180, 103, 124, 351, 353, 74, 318, 50, 77, 62, 127, 64, 325]. Special [200]. Specification [49]. Specified [38, 87, 333]. Spectral [91, 336]. Squares [193, 188, 369, 88, 113, 179, 207, 235, 272]. Stability [297, 22, 300, 53, 310, 27, 105, 340, 281]. Stable [186, 367]. Stably [89]. Stage [243]. Standard [171]. State [379]. Storage [135, 146, 360, 211]. strength [383]. Structured [130]. Structures [50]. Studio [269]. Study [217, 176]. Style [75, 161, 334]. Subprograms [100, 37, 311, 73, 330, 290]. subroutine [211]. Subset [167]. Subspace [354]. Subspaces [38, 25, 302]. Suite [9]. SUMMA [96, 342]. Sunriver [377]. Supercomputing [371, 381]. Supernodal [103, 124, 351, 353]. Support [249, 269]. SVD [4, 169, 170, 166]. SVDs [130]. Swapping [54, 306]. Switzerland [370]. Sylvester [75, 334]. Symbolic [263]. Symmetric [150, 168, 4, 86, 183, 182, 17, 253, 243, 172, 69, 132, 197, 260]. Symposium [380, 374, 375]. System [23, 308, 255, 251, 141, 265, 245, 28, 293]. System/ 6000 [28, 293]. Systems [142, 143, 350, 76, 81, 125, 4, 62, 184, 175, 267, 221, 240, 210, 260, 326, 261, 264, 256, 216, 339]. systolic [276].

Tall [224]. Task [232, 97, 221]. Technical [109]. techniques [207, 245]. Templates [106, 320, 99]. Terms [279]. Test [123, 9, 290]. Testing [10, 182, 138, 149, 364]. Theory [13, 42, 87, 84, 85, 348, 354, 156, 312, 333]. Third [383]. Tight [163]. Tile [258, 222, 242, 229, 246, 243, 240]. Tiled [191, 190, 368, 260]. Tiles [214, 208]. Time [280, 234]. TN [378]. Tolerance [205, 252]. Tolerant [380, 90, 324]. Tools [6, 285, 378, 179]. topology [254]. total [235]. Townsend [378]. Tracking [232]. Trading [53, 310]. Transformations [284, 214]. Transient [278]. Transpose [65, 314]. Tree [194]. Triangular [36, 198]. Tridiagonal [92, 125, 45, 183, 17, 243, 172, 132, 197, 313, 321]. tune [234]. Tuned [131, 349]. Tuning [187, 108, 212]. Twenty [380]. Twenty-fifth [380]. Two [37, 311, 214, 209, 243]. Two-Sided [209, 214]. Two-Stage [243].

Underdetermined [23, 308]. Unified [268]. Unitary [72, 335, 83, 341]. Units [257]. Universal [57, 315, 96, 342]. Unix [10, 81]. Unsymmetric [79, 332]. Upper [68, 219]. Upper-Hessenberg [68]. USA [384, 378, 376]. Use [108]. User [98, 94]. Using [207, 284, 261, 264, 180, 21, 174, 184, 197, 166, 245, 111, 258, 253, 214, 208, 246, 243, 12, 202].

V [98, 102]. v1.1 [94]. VA [376]. Value [46, 236, 11, 292, 119, 88, 282, 348, 115, 305, 352]. Values [3, 48, 307]. VAPP [370]. Variants [19, 279, 173, 78]. Variations [84, 85, 348, 354]. Vector [189, 370, 316, 202]. Version [114, 158, 140, 262]. Versions [10]. via [59, 317, 254]. Virginia [373, 374]. Visual [269]. vs [280]. weighted [145]. while [180]. Williamsburg [373]. Windsor [375]. Within [291, 232, 271]. Workshop [34, 378, 109, 383, 382].

xHSEQR [187].

York [371].

Zurich [370].

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Dongarra:1987:BRM

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Demmel:1988:CSS

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Bischof:1988:PC

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Brewer:1988:TAAa

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Barlow:1988:CAE

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Bai:1989:BIHa

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Demmel:1989:TMG

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Anderson:1989:ITI

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Deift:1989:BSV

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Mayes:1989:BCF

[12] P. Mayes and G. Radicati. Banded Cholesky factorization using level 3 BLAS. LAPACK Working Note 12, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439-4801, USA, August 1989. URL http:/

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Bai:1989:CNE

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Demmel:1989:FPE

[14] J. Demmel. On floating point errors in Cholesky. LAPACK Working Note 14, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, October 1989. URL http:/

/www.netlib.org/lapack/lawns/lawn14.ps;   http://www.netlib.
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Demmel:1989:JMM

[15] J. Demmel and K. Veselic. Jacobi’s method is more accurate than QR. LAPACK Working Note 15, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Octo-

ber 1989. URL http://www.netlib.org/lapack/lawns/lawn15.ps;
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Anderson:1989:RIR

[16] E. Anderson and J. Dongarra. Results from the initial release of LA-PACK. LAPACK Working Note 16, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Novem-

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November 1989. (Replaced by LAWN 41 or 81!!).

Greenbaum:1989:EQQ

[17] A. Greenbaum and J. Dongarra. Experiments with QR/QL methods for the symmetric tridiagonal eigenproblem. LAPACK Working Note 17, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, November 1989. URL http:/

/www.netlib.org/lapack/lawns/lawn17.ps;   http://www.netlib.
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Anderson:1990:IGL

[18] E. Anderson and J. Dongarra. Implementation guide for LAPACK. LAPACK Working Note 18, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, April 1990.

URL http://www.netlib.org/lapack/lawns/lawn18.ps;   http://
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Anderson:1990:EBA

[19] E. Anderson and J. Dongarra. Evaluating block algorithm variants in LAPACK. LAPACK Working Note 19, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

April 1990. URL http://www.netlib.org/lapack/lawns/lawn19.ps;
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103, April 1990.

Anderson:1990:LPLa

[20] E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen. LA-PACK: A portable linear algebra library for high-performance computers. LAPACK Working Note 20, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

May 1990. URL http://www.netlib.org/lapack/lawns/lawn20.ps;
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105, May 1990. Published in [288].

Croz:1990:FBM

[21] Jeremy Du Croz, Peter Mayes, and Giuseppe Radicati. Factorizations of band matrices using level 3 BLAS. LAPACK Working Note 21, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, July 1990. URL http:/

/www.netlib.org/lapack/lawns/lawn21.ps;   http://www.netlib.
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Demmel:1990:SBA

[22] J. Demmel and N. Higham. Stability of block algorithms with fast level 3 BLAS. LAPACK Working Note 22, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

July 1990. URL http://www.netlib.org/lapack/lawns/lawn22.ps;
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110, July 1990. Published in [300].

Demmel:1990:IEB

[23] J. Demmel and N. Higham. Improved error bounds for underdetermined system solvers. LAPACK Working Note 23, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

August 1990. URL http://www.netlib.org/lapack/lawns/lawn23.ps;
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113, August 1990. Published in [308].

Dongarra:1990:LBF

[24] J. Dongarra and S. Ostrouchov. LAPACK block factorization algorithms on the Intel iPSC/860. LAPACK Working Note 24, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996,

USA, October 1990. URL http://www.netlib.org/lapack/lawns/
lawn24.ps;   http://www.netlib.org/lapack/lawnspdf/lawn24.pdf.

UT-CS-90-115, October, 1990.

Dongarra:1990:NCC

[25] J. Dongarra, S. Hammarling, and J. Wilkinson. Numerical considerations in computing invariant subspaces. LAPACK Working Note 25, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, October 1990. URL http:/

/www.netlib.org/lapack/lawns/lawn25.ps;   http://www.netlib.

org/lapack/lawnspdf/lawn25.pdf. UT-CS-90-117, October, 1990. Published in [302].

Anderson:1990:PEL

[26] E. Anderson, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, S. Hammarling, and W. Kahan. Prospectus for an extension to LAPACK: A portable linear algebra library for high-performance computers. LA-PACK Working Note 26, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, November

1990. 10 pp. URL http://www.netlib.org/lapack/lawns/lawn26.ps;
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118, November 1990.

DuCroz:1990:SMM

[27] J. Du Croz and N. Higham. Stability of methods for matrix inversion. LAPACK Working Note 27, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Oc-

tober 1990. URL http://www.netlib.org/lapack/lawns/lawn27.ps;
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119, October, 1990. Published in [297].

Dongarra:1990:IRS

[28] J. Dongarra, P. Mayes, and G. Radicati. The IBM RISC System/6000 and linear algebra operations. LAPACK Working Note 28, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN

37996, USA, December 1990. URL http://www.netlib.org/lapack/
lawns/lawn28.ps;   http://www.netlib.org/lapack/lawnspdf/lawn28.

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vandeGeijn:1991:GCO

[29] R. van de Geijn. On global combine operations. LAPACK Working Note 29, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, April 1991. URL http:/

/www.netlib.org/lapack/lawns/lawn29.ps;   http://www.netlib.
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lished in [319].

Dongarra:1991:RCF

[30] J. Dongarra and R. van de Geijn. Reduction to condensed form for the eigenvalue problem on distributed memory architectures. LAPACK Working Note 30, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, April 1991. URL http:/

/www.netlib.org/lapack/lawns/lawn30.ps;   http://www.netlib.
org/lapack/lawnspdf/lawn30.pdf. UT-CS-91-130, April 1991. Pub-

lished in [303].

Anderson:1991:GQF

[31] E. Anderson, Z. Bai, and J. Dongarra. Generalized QR factorization and its applications. LAPACK Working Note 31, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

April 1991. URL http://www.netlib.org/lapack/lawns/lawn31.ps;
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131, April 1991. Published in [294].

Bischof:1991:GIC

[32] C. Bischof and P. T. P. Tang. Generalized incremental condition estimation. LAPACK Working Note 32, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

May 1991. URL http://www.netlib.org/lapack/lawns/lawn32.ps;
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132, May 1991. Published in [295].

Bischof:1991:RIC

[33] C. Bischof and P. T. P. Tang. Robust incremental condition estimation. LAPACK Working Note 33, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

May 1991. URL http://www.netlib.org/lapack/lawns/lawn33.ps;
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133, May 1991.

Dongarra:1991:WB

[34] J. J. Dongarra. Workshop on the BLACS. LAPACK Working Note 34, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, May 1991. URL http:/

/www.netlib.org/lapack/lawns/lawn34.ps;   http://www.netlib.
org/lapack/lawnspdf/lawn34.pdf. UT-CS-91-134, May 1991.

Anderson:1991:IGL

[35] E. Anderson, J. Dongarra, and S. Ostrouchov. Implementation guide for LAPACK. LAPACK Working Note 35, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

August 1991. URL http://www.netlib.org/lapack/lawns/lawn35.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn35.pdf. UT-CS-91-

138, August 1991.

Anderson:1991:RTS

[36] E. Anderson. Robust triangular solvers. LAPACK Working Note 36, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, August 1991. URL http://www.netlib.org/

lapack/lawns/lawn36.ps;   http://www.netlib.org/lapack/lawnspdf/

lawn36.pdf. UT-CS-91-142, August, 1991.

Dongarra:1991:TDB

[37] Jack J. Dongarra and Robert A. van de Geijn. Two dimensional basic linear algebra communication subprograms. LAPACK Working Note 37, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, October 1991. URL http:/

/www.netlib.org/lapack/lawns/lawn37.ps;   http://www.netlib.

org/lapack/lawnspdf/lawn37.pdf. UT-CS-91-138, October, 1991. Published in [311].

Bai:1991:DAC

[38] Zhaojun Bai and James W. Demmel. On a direct algorithm for computing invariant subspaces with specified eigenvalues. LAPACK Working Note 38, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, November 1991. URL http:/

/www.netlib.org/lapack/lawns/lawn38.ps;   http://www.netlib.
org/lapack/lawnspdf/lawn38.pdf. UT-CS-91-139, November, 1991.

Demmel:1991:DPH

[39] James Demmel, Jack Dongarra, and W. Kahan. On designing portable high performance numerical libraries. LAPACK Working Note 39, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, July 1991. URL http:/

/www.netlib.org/lapack/lawns/lawn39.ps;   http://www.netlib.
org/lapack/lawnspdf/lawn39.pdf. UT-CS-91-141, July, 1991. Pub-

lished in [298].

Demmel:1992:BLF

[40] James Demmel, Nick Higham, and Rob Schreiber. Block LU factorization. LAPACK Working Note 40, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Febru-

ary 1992. URL http://www.netlib.org/lapack/lawns/lawn40.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn40.pdf. UT-CS-92-

149, February 1992.

Blackford:1992:IGL

[41] Susan Blackford and Jack Dongarra. Installation guide for LA-PACK. LAPACK Working Note 41, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

March 1992. URL http://www.netlib.org/lapack/lawns/lawn41.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn41.pdf. UT-CS-92-

151, March, 1992.

Higham:1992:PTB

[42] Nick Higham. Perturbation theory and backward error for AX − XB = C. LAPACK Working Note 42, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

April 1992. URL http://www.netlib.org/lapack/lawns/lawn42.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn42.pdf. UT-CS-92-

153, April, 1992. Published in [312].

Dongarra:1992:LSD

[43] Jack Dongarra, Robert van de Geijn, and David Walker. A look at scalable dense linear algebra libraries. LAPACK Working Note 43, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, April 1992. URL http:/

/www.netlib.org/lapack/lawns/lawn43.ps;   http://www.netlib.
org/lapack/lawnspdf/lawn43.pdf. UT-CS-92-155, April, 1992. Pub-

lished in [301].

Anderson:1992:PLP

[44] Edward Anderson and Jack Dongarra. Performance of LAPACK: A portable library of numerical linear algebra routines. LAPACK Working Note 44, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, May 1992. URL http:/

/www.netlib.org/lapack/lawns/lawn44.ps;   http://www.netlib.
org/lapack/lawnspdf/lawn44.pdf. UT-CS-92-156, May 1992. Pub-

lished in [304].

Demmel:1992:III

[45] J. Demmel. The inherent inaccuracy of implicit tridiagonal QR. LA-PACK Working Note 45, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, May 1992. URL http:/

/www.netlib.org/lapack/lawns/lawn45.ps;   http://www.netlib.
org/lapack/lawnspdf/lawn45.pdf. UT-CS-92-162, May 1992.

Bai:1992:CGS

[46] Z. Bai and J. Demmel. Computing the generalized singular value decomposition. LAPACK Working Note 46, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

May 1992. URL http://www.netlib.org/lapack/lawns/lawn46.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn46.pdf. UT-CS-92-

163, May 1992. Published in [305].

Demmel:1992:OPN

[47] J. Demmel. Open problems in numerical linear algebra. LAPACK Working Note 47, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, May 1992. URL http:/

/www.netlib.org/lapack/lawns/lawn47.ps;   http://www.netlib.
org/lapack/lawnspdf/lawn47.pdf. UT-CS-92-164, May 1992.

Demmel:1992:CAS

[48] J. Demmel and W. Gragg. On computing accurate singular values and eigenvalues of matrices with acyclic graphs. LAPACK Working Note 48, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, May 1992. URL http:/

/www.netlib.org/lapack/lawns/lawn48.ps;   http://www.netlib.
org/lapack/lawnspdf/lawn48.pdf. UT-CS-92-166, May 1992. Pub-

lished in [307].

Demmel:1992:SFP

[49] J. Demmel. A specification for floating point parallel prefix. LAPACK Working Note 49, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, May 1992. URL http:/

/www.netlib.org/lapack/lawns/lawn49.ps;   http://www.netlib.
org/lapack/lawnspdf/lawn49.pdf. UT-CS-92-167, May 1992.

Eijkhout:1992:DSD

[50] Victor Eijkhout. Distributed sparse data structures for linear algebra operations. LAPACK Working Note 50, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

May 1992. URL http://www.netlib.org/lapack/lawns/lawn50.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn50.pdf. UT-CS-92-

169, May 1992.

Eijkhout:1992:QPC

[51] Victor Eijkhout. Qualitative properties of the conjugate gradient and Lanczos methods in a matrix framework. LAPACK Working Note 51, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, May 1992. URL http:/

/www.netlib.org/lapack/lawns/lawn51.ps;   http://www.netlib.
org/lapack/lawnspdf/lawn51.pdf. UT-CS-92-170, May 1992.

Heath:1992:CPN

[52] Michael T. Heath and Padma Raghavan. A Cartesian parallel nested dissection algorithm. LAPACK Working Note 52, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

June 1992. URL http://www.netlib.org/lapack/lawns/lawn52.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn52.pdf. UT-CS-92-

178, June 1992. Published in [323].

Demmel:1992:TPN

[53] J. W. Demmel. Trading off parallelism and numerical stability. LA-PACK Working Note 53, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, June 1992.

URL http://www.netlib.org/lapack/lawns/lawn53.ps;   http://
www.netlib.org/lapack/lawnspdf/lawn53.pdf. UT-CS-92-179, June

1992. Published in [310].

Bai:1992:SDB

[54] Z. Bai and J. W. Demmel. On swapping diagonal blocks in real Schur form. LAPACK Working Note 54, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Oc-

tober 1992. URL http://www.netlib.org/lapack/lawns/lawn54.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn54.pdf. UT-CS-92-

182, October 1992. Published in [306].

Choi:1992:SSLa

[55] J. Choi, J. Dongarra, R. Pozo, and D. Walker. ScaLAPACK: A scalable linear algebra for distributed memory concurrent computers. LAPACK Working Note 55, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Novem-

ber 1992. URL http://www.netlib.org/lapack/lawns/lawn55.ps;

 http://www.netlib.org/lapack/lawnspdf/lawn55.pdf. UT-CS-92-

181, November 1992. Published in [296].

DAzevedo:1993:RCC

[56] E. F. D’Azevedo, V. L. Eijkhout, and C. H. Romine. Reducing communication costs in the conjugate gradient algorithm on distributed memory multiprocessors. LAPACK Working Note 56, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

January 1993. URL http://www.netlib.org/lapack/lawns/lawn56.
ps;   http://www.netlib.org/lapack/lawnspdf/lawn56.pdf. UT-

CS-93-185, January 1993.

Choi:1993:PPU

[57] Jaeyoung Choi, Jack J. Dongarra, and David W. Walker. PUMMA: Parallel Universal Matrix Multiplication Algorithms on distributed memory concurrent computers. LAPACK Working Note 57, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996,

USA, May 1993. URL http://www.netlib.org/lapack/lawns/lawn57.
ps;   http://www.netlib.org/lapack/lawnspdf/lawn57.pdf. UT-

CS-93-187, May 1993. Published in [315].

Dongarra:1993:DLA

[58] Jack Dongarra and David Walker. The design of linear algebra libraries for high performance computer. LAPACK Working Note 58, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, June 1993. URL http:/

/www.netlib.org/lapack/lawns/lawn58.ps;   http://www.netlib.
org/lapack/lawnspdf/lawn58.pdf. UT-CS-93-188, June 1993.

Demmel:1993:FNA

[59] James W. Demmel and Xiaoye Li. Faster numerical algorithms via exception handling. LAPACK Working Note 59, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

March 1993. URL http://www.netlib.org/lapack/lawns/lawn59.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn59.pdf. UT-CS-93-

192, March 1993. Published in [317].

Demmel:1993:PNLa

[60] James W. Demmel, Michael T. Heath, and Henk A. van der Vorst. Parallel numerical linear algebra. LAPACK Working Note 60, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN

37996, USA, March 1993. URL http://www.netlib.org/lapack/lawns/

lawn60.ps;   http://www.netlib.org/lapack/lawnspdf/lawn60.pdf.

UT-CS-93-192, March 1993. Published in [309].

Dongarra:1993:OOD

[61] J. Dongarra, R. Pozo, and D. Walker. An object oriented design for high performance linear algebra on distributed memory architectures. LAPACK Working Note 61, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Au-

gust 1993. URL http://www.netlib.org/lapack/lawns/lawn61.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn61.pdf. UT-CS-93-

200, August 1993.

Heath:1993:DSS

[62] Michael T. Heath and Padma Raghavan. Distributed solution of sparse linear systems. LAPACK Working Note 62, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

August 1993. URL http://www.netlib.org/lapack/lawns/lawn62.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn62.pdf. UT-CS-93-

201, August 1993.

Heath:1993:LPS

[63] Michael T. Heath and Padma Raghavan. Line and plane separators. LAPACK Working Note 63, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Au-

gust 1993. URL http://www.netlib.org/lapack/lawns/lawn63.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn63.pdf. UT-CS-93-

202, August 1993.

Raghavan:1993:DSG

[64] Padma Raghavan. Distributed sparse Gaussian elimination and orthogonal factorization. LAPACK Working Note 64, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

August 1993. URL http://www.netlib.org/lapack/lawns/lawn64.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn64.pdf. UT-CS-93-

203, August 1993. Published in [325].

Choi:1993:PMT

[65] Jaeyoung Choi, Jack J. Dongarra, and David W. Walker. Parallel matrix transpose algorithms on distributed memory concurrent computers. LAPACK Working Note 65, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Novem-

ber 1993. URL http://www.netlib.org/lapack/lawns/lawn65.ps;

 http://www.netlib.org/lapack/lawnspdf/lawn65.pdf. UT-CS-93-

215, November, 1993. Published in [314].

Eijkhout:1993:CPI

[66] Victor Eijkhout. A characterization of polynomial iterative methods. LAPACK Working Note 66, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Novem-

ber 1993. URL http://www.netlib.org/lapack/lawns/lawn66.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn66.pdf. UT-CS-93-

216, November 1993.

Desprez:1993:PCF

[67] F. Desprez, J. Dongarra, and B. Tourancheau. Performance complexity of LU factorization with efficient pipelining and overlap on a multiprocessor. LAPACK Working Note 67, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, De-

cember 1993. URL http://www.netlib.org/lapack/lawns/lawn67.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn67.pdf. UT-CS-93-

218, December, 1993.

Berry:1994:HPA

[68] Michael W. Berry, Jack J. Dongarra, and Youngbae Kim. A highly parallel algorithm for the reduction of a nonsymmetric matrix to block upper-Hessenberg form. LAPACK Working Note 68, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

February 1994. URL http://www.netlib.org/lapack/lawns/lawn68.
ps;   http://www.netlib.org/lapack/lawnspdf/lawn68.pdf. UT-

CS-94-221, February 1994.

Rutter:1994:SIC

[69] J. Rutter. A serial implementation of Cuppen’s divide and conquer algorithm for the symmetric eigenvalue problem. LAPACK Working Note 69, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, March 1994. URL http:/

/www.netlib.org/lapack/lawns/lawn69.ps;   http://www.netlib.
org/lapack/lawnspdf/lawn69.pdf. UT-CS-94-225, March 1994.

Demmel:1994:CPB

[70] James Demmel, Inderjit Dhillon, and Huan Ren. On the correctness of parallel bisection in floating point. LAPACK Working Note 70, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, March 1994. URL http:/

/www.netlib.org/lapack/lawns/lawn70.ps;   http://www.netlib.

org/lapack/lawnspdf/lawn70.pdf. UT-CS-94-228, March 1994. Pub-

lished in [322].

Dongarra:1994:IRP

[71] Jack Dongarra and Michael Kolatis. IBM RS/6000-550 & -590 performance for selected routines in ESSL. LAPACK Working Note 71, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, April 1994. URL http:/

/www.netlib.org/lapack/lawns/lawn71.ps;   http://www.netlib.
org/lapack/lawnspdf/lawn71.pdf. UT-CS-94-231, April 1994.

Lehoucq:1995:CEU

[72] R. Lehoucq. The computation of elementary unitary matrices. LA-PACK Working Note 72, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Octo-

ber 1995. URL http://www.netlib.org/lapack/lawns/lawn72.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn72.pdf. UT-CS-94-

233, October 1995. Published in [335].

Whaley:1994:BLA

[73] R. Clint Whaley. Basic linear algebra communication subprograms: Analysis and implementation across multiple parallel architectures. LAPACK Working Note 73, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, May 1994. URL http:/

/www.netlib.org/lapack/lawns/lawn73.ps;   http://www.netlib.
org/lapack/lawnspdf/lawn73.pdf. UT-CS-94-234, May 1994.

Dongarra:1994:SMLa

[74] J. Dongarra, A. Lumsdaine, X. Niu, R. Pozo, and K. Remington. A sparse matrix library in C++ for high performance architectures. LAPACK Working Note 74, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

July 1994. URL http://www.netlib.org/lapack/lawns/lawn74.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn74.pdf. UT-CS-94-

236, July 1994. Published in [318].

Kaagstrom:1994:LSA

[75] Bo Kågström and Peter Poromaa. LAPACK-style algorithms and software for solving the generalized Sylvester equation and estimating the separating between regular matrix pairs. LAPACK Working Note 75, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, July 1994. URL http:/

/www.netlib.org/lapack/lawns/lawn75.ps;   http://www.netlib.

org/lapack/lawnspdf/lawn75.pdf. UT-CS-94-237, July 1994. Pub-

lished in [334].

Barrett:1994:ABI

[76] Richard Barrett, Michael Berry, Jack Dongarra, Victor Eijkhout, and Charles Romine. Algorithmic bombardment for the iterative solution of linear systems: A poly-iterative approach. LAPACK Working Note 76, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, August 1994. URL http:/

/www.netlib.org/lapack/lawns/lawn76.ps;   http://www.netlib.
org/lapack/lawnspdf/lawn76.pdf. UT-CS-94-239, August, 1994. Pub-

lished in [326].

Eijkhout:1994:BCD

[77] Victor Eijkhout and Roldan Pozo. Basic concepts for distributed sparse linear algebra operations. LAPACK Working Note 77, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN

37996, USA, August 1994. URL http://www.netlib.org/lapack/
lawns/lawn77.ps;   http://www.netlib.org/lapack/lawnspdf/lawn77.

pdf. UT-CS-94-240, August, 1994.

Eijkhout:1994:CVC

[78] Victor Eijkhout. Computational variants of the CGS and BiCGstab methods. LAPACK Working Note 78, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

August 1994. URL http://www.netlib.org/lapack/lawns/lawn78.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn78.pdf. UT-CS-94-

241, August, 1994.

Henry:1994:PQA

[79] Greg Henry and Robert van de Geijn. Parallelizing the QR algorithm for the unsymmetric algebraic eigenvalue problem: Myths and reality. LAPACK Working Note 79, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Au-

gust 1994. URL http://www.netlib.org/lapack/lawns/lawn79.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn79.pdf. UT-CS-94-

244, August, 1994. Published in [332].

Choi:1994:DIS

[80] J. Choi, J. J. Dongarra, S. Ostrouchov, A. P. Petitet, D. W. Walker, and R. C. Whaley. The design and implementation of the ScaLA-PACK LU, QR, and Cholesky factorization routines. LAPACK Working Note 80, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, September 1994. URL http:/

/www.netlib.org/lapack/lawns/lawn80.ps;   http://www.netlib.
org/lapack/lawnspdf/lawn80.pdf. UT-CS-94-246, September, 1994.

Published in [329].

Blackford:1994:QIG

[81] S. Blackford and J. Dongarra. Quick installation guide for LAPACK on Unix systems. LAPACK Working Note 81, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

September 1994. URL http://www.netlib.org/lapack/lawns/lawn81.
ps;   http://www.netlib.org/lapack/lawnspdf/lawn81.pdf. UT-

CS-94-249, September, 1994.

Dongarra:1994:CCI

[82] J. Dongarra and M. Kolatis. Call conversion interface (CCI) for LA-PACK/ESSL. LAPACK Working Note 82, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

August 1994. URL http://www.netlib.org/lapack/lawns/lawn82.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn82.pdf. UT-CS-94-

250, August, 1994.

Li:1994:RPB

[83] Ren-Cang Li. Relative perturbation bounds for the unitary polar factor. LAPACK Working Note 83, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Septem-

ber 1994. URL http://www.netlib.org/lapack/lawns/lawn83.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn83.pdf. UT-CS-94-

251, September, 1994. Published in [341].

Li:1994:RPTa

[84] Ren-Cang Li. Relative perturbation theory: (I) eigenvalue variations. LAPACK Working Note 84, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Septem-

ber 1994. URL http://www.netlib.org/lapack/lawns/lawn84.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn84.pdf. UT-CS-94-

252, September, 1994. Published in [348].

Li:1994:RPTb

[85] Ren-Cang Li. Relative perturbation theory: (II) eigenspace variations. LAPACK Working Note 85, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Septem-

ber 1994. URL http://www.netlib.org/lapack/lawns/lawn85.ps;

 http://www.netlib.org/lapack/lawnspdf/lawn85.pdf. UT-CS-94-

253, September, 1994. Published in [354].

Demmel:1994:PFE

[86] J. Demmel and K. Stanley. The performance of finding eigenvalues and eigenvectors of dense symmetric matrices on distributed memory computers. LAPACK Working Note 86, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Septem-

ber 1994. URL http://www.netlib.org/lapack/lawns/lawn86.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn86.pdf. UT-CS-94-

254, September, 1994.

Kaagstrom:1994:CES

[87] B. Kågström and P. Poromaa. Computing eigenspaces with specified eigenvalues of a regular matrix pair (A,B) and condition estimation: Theory, algorithms and software. LAPACK Working Note 87, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, September 1994. URL http:/

/www.netlib.org/lapack/lawns/lawn87.ps;   http://www.netlib.
org/lapack/lawnspdf/lawn87.pdf. UT-CS-94-255, September, 1994.

Published in [333].

Gu:1994:ECS

[88] Ming Gu, James Demmel, and Inderjit Dhillon. Efficient computation of the singular value decomposition with applications to least squares problems. LAPACK Working Note 88, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Oc-

tober 1994. URL http://www.netlib.org/lapack/lawns/lawn88.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn88.pdf. UT-CS-94-

257, October, 1994.

Li:1994:SSE

[89] Ren-Cang Li. Solving secular equations stably and efficiently. LA-PACK Working Note 89, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Novem-

ber 1994. URL http://www.netlib.org/lapack/lawns/lawn89.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn89.pdf. UT-CS-94-

260, November, 1994.

Plank:1994:ABD

[90] J. S. Plank, Y. Kim, and J. J. Dongarra. Algorithm-based diskless checkpointing for fault tolerant matrix operations. LAPACK Working Note 90, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, December 1994. URL http:/

/www.netlib.org/lapack/lawns/lawn90.ps;   http://www.netlib.
org/lapack/lawnspdf/lawn90.pdf. UT-CS-94-268, December 1994.

Published in [324].

Bai:1995:SDN

[91] Z. Bai, J. Demmel, J. Dongarra, A. Petitet, H. Robinson, and K. Stanley. The spectral decomposition of nonsymmetric matrices on distributed memory parallel computers. LAPACK Working Note 91, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, January 1995. URL http:/

/www.netlib.org/lapack/lawns/lawn91.ps;   http://www.netlib.
org/lapack/lawnspdf/lawn91.pdf. UT-CS-95-273, January 1995. Pub-

lished in [336].

Choi:1995:DPDa

[92] J. Choi, J. Dongarra, and D. Walker. The design of a parallel dense linear algebra software library: Reduction to Hessenberg, tridiagonal, and bidiagonal form. LAPACK Working Note 92, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

February 1995. URL http://www.netlib.org/lapack/lawns/lawn92.
ps;   http://www.netlib.org/lapack/lawnspdf/lawn92.pdf. UT-

CS-95-275, February 1995. Published in [313, 321].

Choi:2001:IGS

[93] J. Choi, J. Demmel, I. Dhillon, J. Dongarra, S. Ostrouchov, A. Petitet, K. Stanley, D. Walker, and R. C. Whaley. Installation guide for ScaLA-PACK. LAPACK Working Note 93, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, August

31, 2001. URL http://www.netlib.org/lapack/lawns/lawn93.ps;
http://www.netlib.org/lapack/lawnspdf/lawn93.pdf. Updated Au-

gust 31, 2001 (Version 1.7).

Dongarra:1997:UGB

[94] J. Dongarra and R. C. Whaley. A user’s guide to the BLACS v1.1. LAPACK Working Note 94, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, May

5, 1997. URL http://www.netlib.org/lapack/lawns/lawn94.ps;
http://www.netlib.org/lapack/lawnspdf/lawn94.pdf. Updated May

5, 1997 (Version 1.1).

Choi:1995:SPL

[95] J. Choi, J. Demmel, I. Dhillon, J. Dongarra, S. Ostrouchov, A. Petitet, K. Stanley, D. Walker, and R. C. Whaley. ScaLAPACK: A portable linear algebra library for distributed memory computers — design issues and performance. LAPACK Working Note 95, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

March 1995. URL http://www.netlib.org/lapack/lawns/lawn95.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn95.pdf. UT-CS-95-

283, March 1995. Published in [328].

vandeGeijn:1995:SSU

[96] R. A. van de Geijn and J. Watts. SUMMA: Scalable Universal Matrix Multiplication Algorithm. LAPACK Working Note 96, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN

37996, USA, April 1995. URL http://www.netlib.org/lapack/lawns/
lawn96.ps;   http://www.netlib.org/lapack/lawnspdf/lawn96.pdf.

UT-CS-95-286, April 1995. Published in [342].

Chakrabarti:1995:MBM

[97] S. Chakrabarti, J. Demmel, and D. Yelick. Modeling the benefits of mixed data and task parallelism. LAPACK Working Note 97, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN

37996, USA, May 1995. URL http://www.netlib.org/lapack/lawns/
lawn97.ps;   http://www.netlib.org/lapack/lawnspdf/lawn97.pdf.

UT-CS-95-289, May 1995.

Dongarra:1995:LVH

[98] J. Dongarra, R. Pozo, and D. Walker. LAPACK++ V. 1.0: High performance linear algebra users’ guide. LAPACK Working Note 98, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, May 1995. URL http:/

/www.netlib.org/lapack/lawns/lawn98.ps;   http://www.netlib.
org/lapack/lawnspdf/lawn98.pdf. UT-CS-95-290, May 1995.

Dongarra:1995:RCI

[99] J. Dongarra, V. Eijkhout, and A. Kalhan. Reverse communication interface for linear algebra templates for iterative methods. LAPACK Working Note 99, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, May 1995. URL http:/

/www.netlib.org/lapack/lawns/lawn99.ps;   http://www.netlib.
org/lapack/lawnspdf/lawn99.pdf. UT-CS-95-291, May 1995.

Choi:1995:PSP

[100] J. Choi, J. Dongarra, S. Ostrouchov, A. Petitet, D. Walker, and R. C. Whaley. A proposal for a set of parallel basic linear algebra subprograms. LAPACK Working Note 100, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, May 1995.

URL http://www.netlib.org/lapack/lawns/lawn100.ps;   http://
www.netlib.org/lapack/lawnspdf/lawn100.pdf. UT-CS-95-292, May

1995. Published in [100].

Dongarra:1995:PFI

[101] J. J. Dongarra, J. Du Croz, S. Hammarling, J. Waśniewski, and A. Zemla. A proposal for a Fortran 90 interface for LAPACK. LA-PACK Working Note 101, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, July 1995.

URL http://www.netlib.org/lapack/lawns/lawn101.ps;   http://
www.netlib.org/lapack/lawnspdf/lawn101.pdf. UT-CS-95-295, July

1995. Published in [331].

Dongarra:1995:IVI

[102] J. Dongarra, A. Lumsdaine, R. Pozo, and K. Remington. IML++ v. 1.2: Iterative methods library reference guide. LAPACK Working Note 102, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, August 1995. URL http://www.netlib.

org/lapack/lawns/lawn102.ps;   http://www.netlib.org/lapack/

lawnspdf/lawn102.pdf. UT-CS-95-303, August 1995.

Demmel:1995:SAS

[103] J. W. Demmel, S. C. Eisenstat, J. R. Gilbert, X. S. Li, and J. W. H. Liu. A supernodal approach to sparse partial pivoting. LAPACK Working Note 103, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, September 1995. URL http://

www.netlib.org/lapack/lawns/lawn103.ps;   http://www.netlib.
org/lapack/lawnspdf/lawn103.pdf. UT-CS-95-304, September 1995.

Published in [353].

Higham:1995:IRL

[104] N. J. Higham. Iterative refinement and LAPACK. LAPACK Working Note 104, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, October 1995. URL http://www.

netlib.org/lapack/lawns/lawn104.ps;   http://www.netlib.org/

lapack/lawnspdf/lawn104.pdf. UT-CS-95-308, October 1995. Published in [339].

Higham:1995:SDP

[105] N. J. Higham. Stability of the diagonal pivoting method with partial pivoting. LAPACK Working Note 105, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Oc-

tober 1995. URL http://www.netlib.org/lapack/lawns/lawn105.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn105.pdf. UT-CS-95-

309, October 1995. Published in [340].

Bai:1995:TLAa

[106] Z. Bai, D. Day, J. Demmel, J. Dongarra, M. Gu, A. Ruhe, and H. van der Vorst. Templates for linear algebra problems. LA-PACK Working Note 106, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, October 1995.

URL http://www.netlib.org/lapack/lawns/lawn106.ps;   http://
www.netlib.org/lapack/lawnspdf/lawn106.pdf. UT-CS-95-311, Octo-

ber 1995. Published in [320].

Kaagstrom:1995:GBLa

[107] B. Kågström, P. Ling, and C. Van Loan. GEMM-based level 3 BLAS: High-performance model implementations and performance evaluation benchmark. LAPACK Working Note 107, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996,

USA, November 1995. URL http://www.netlib.org/lapack/lawns/
lawn107.ps;   http://www.netlib.org/lapack/lawnspdf/lawn107.

pdf. UT-CS-95-315, November 1995. Published in [347].

Kaagstrom:1995:GBLb

[108] B. Kågström, P. Ling, and C. Van Loan. GEMM-based level 3 BLAS: Installation, tuning and use of the model implementations and the performance evaluation benchmark. LAPACK Working Note 108, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, November 1995. URL http://www.netlib.

org/lapack/lawns/lawn108.ps;   http://www.netlib.org/lapack/

lawnspdf/lawn108.pdf. UT-CS-95-316, November 1995.

Dongarra:1995:BTW

[109] J. Dongarra, S. Hammarling, and S. Ostrouchov. BLAS technical workshop. LAPACK Working Note 109, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Novem-

ber 1995. URL http://www.netlib.org/lapack/lawns/lawn109.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn109.pdf. UT-CS-95-

317, November 1995.

Dongarra:1996:KCP

[110] J. J. Dongarra, S. Hammarling, and D. W. Walker. Key concepts for parallel out-of-core LU factorization. LAPACK Working Note 110, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN

37996, USA, April 1996. URL http://www.netlib.org/lapack/lawns/
lawn110.ps;   http://www.netlib.org/lapack/lawnspdf/lawn110.

pdf. UT-CS-96-324, April 1996. Published in [338].

Bilmes:1996:OMM

[111] J. Bilmes, K. Asanovic, J. Demmel, D. Lam, and C.-W. Chin. Optimizing matrix multiply using PHiPAC: a portable, high-performance, ANSI C coding methodology. LAPACK Working Note 111, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN

37996, USA, May 1996. URL http://www.netlib.org/lapack/lawns/
lawn111.ps;   http://www.netlib.org/lapack/lawnspdf/lawn111.

pdf. UT-CS-96-326, May 1996.

Blackford:1996:PEDa

[112] L. S. Blackford, A. Cleary, J. Demmel, I. Dhillon, J. Dongarra, S. Hammarling, A. Petitet, H. Ren, K. Stanley, and R. C. Whaley. Practical experience in the dangers of heterogeneous computing. LA-PACK Working Note 112, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, July 1996.

URL http://www.netlib.org/lapack/lawns/lawn112.ps;   http://
www.netlib.org/lapack/lawnspdf/lawn112.pdf. UT-CS-96-330, July

1996. Published in [327, 337].

Quintana-Orti:1996:BPA

[113] G. Quintana-Orti, E. S. Quintana-Orti, and A. Petitet. Blockpartitioned algorithms for solving the linear least squares problem. LA-PACK Working Note 113, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, July 1996.

URL http://www.netlib.org/lapack/lawns/lawn113.ps;   http://
www.netlib.org/lapack/lawnspdf/lawn113.pdf. UT-CS-96-333, July

1996.

Quintana-Orti:1996:BVQ

[114] G. Quintana-Orti, X. Sun, and C. Bischof. A BLAS-3 version of the QR factorization with column pivoting. LAPACK Working Note 114, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, August 1996. URL http://www.netlib.

org/lapack/lawns/lawn114.ps;   http://www.netlib.org/lapack/

lawnspdf/lawn114.pdf. UT-CS-96-334, August 1996.

Ren:1996:EAI

[115] H. Ren. On the error analysis and implementation of some eigenvalue decomposition and singular value decomposition algorithms. LA-PACK Working Note 115, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Septem-

ber 1996. URL http://www.netlib.org/lapack/lawns/lawn115.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn115.pdf. UT-CS-96-

336, September 1996.

Sidani:1996:PMD

[116] M. Sidani and B. Harrod. Parallel matrix distributions: Have we been doing it all right? LAPACK Working Note 116, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996,

USA, November 1996. URL http://www.netlib.org/lapack/lawns/
lawn116.ps;   http://www.netlib.org/lapack/lawnspdf/lawn116.

pdf. UT-CS-96-340, November 1996.

Blackford:1996:FIL

[117] L. Susan Blackford, Jack J. Dongarra, Jeremy Du Croz, Sven Hammarling, and Jerzy Waśniewski. A Fortran 90 interface for LAPACK. LA-PACK Working Note 117, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, December 1996.

URL http://www.netlib.org/lapack/lawns/lawn117.ps;   http://
www.netlib.org/lapack/lawnspdf/lawn117.pdf. UT-CS-96-341, De-

cember 1996.

Dongarra:1997:DIP

[118] J. J. Dongarra and E. F. D’Azevedo. The design and implementation of the parallel out-of-core ScaLAPACK LU, QR, and Cholesky factorization routines. LAPACK Working Note 118, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Jan-

uary 1997. URL http://www.netlib.org/lapack/lawns/lawn118.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn118.pdf. UT-CS-97-

347, January 1997. Published in [357].

Demmel:1997:CSV

[119] James Demmel, Ming Gu, Stanley Eisenstat, Ivan Slapničar, Krešimir Veselić, and Zlatko Drmač. Computing the singular value decomposition with high relative accuracy. LAPACK Working Note 119, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, February 1997. URL http://www.netlib.

org/lapack/lawns/lawn119.ps;   http://www.netlib.org/lapack/

lawnspdf/lawn119.pdf. UT-CS-97-348, February 1997. Published in [352].

Desprez:1997:SBC

[120] F. Desprez, J. Dongarra, A. Petitet, C. Randriamaro, and Y. Robert. Scheduling block-cyclic array redistribution. LAPACK Working Note 120, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, February 1997. URL http://www.netlib.

org/lapack/lawns/lawn120.ps;   http://www.netlib.org/lapack/

lawnspdf/lawn120.pdf. UT-CS-97-349, February 1997. Published in [344, 345].

Henry:1997:PIN

[121] G. Henry, D. Watkins, and J. Dongarra. A parallel implementation of the nonsymmetric QR algorithm for distributed memory architectures. LAPACK Working Note 121, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

March 1997. URL http://www.netlib.org/lapack/lawns/lawn121.
ps;   http://www.netlib.org/lapack/lawnspdf/lawn121.pdf. UT-

CS-97-352, March 1997. Published in [363].

Ahues:1997:NDC

[122] M. Ahues and F. Tisseur. A new deflation criterion for the QR algorithm. LAPACK Working Note 122, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

March 1997. URL http://www.netlib.org/lapack/lawns/lawn122.
ps;   http://www.netlib.org/lapack/lawnspdf/lawn122.pdf. UT-

CS-97-353, March 1997.

Bai:1997:TMC

[123] Z. Bai, D. Day, J. Demmel, and J. Dongarra. A test matrix collection for non-Hermitian eigenvalue problems. LAPACK Working Note 123, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, March 1997. URL http://www.netlib.

org/lapack/lawns/lawn123.ps;   http://www.netlib.org/lapack/

lawnspdf/lawn123.pdf. UT-CS-97-355, March 1997.

Demmel:1997:APS

[124] J. Demmel, J. Gilbert, and X. Li. An asynchronous parallel supernodal algorithm for sparse Gaussian elimination. LAPACK Working Note 124, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, April 1997. URL http://www.netlib.

org/lapack/lawns/lawn124.ps;   http://www.netlib.org/lapack/

lawnspdf/lawn124.pdf. UT-CS-97-357, April 1997. Published in [351].

Cleary:1997:ISD

[125] A. Cleary and J. Dongarra. Implementation in ScaLAPACK of divideand-conquer algorithms for banded and tridiagonal linear systems. LA-PACK Working Note 125, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, April 1997.

URL http://www.netlib.org/lapack/lawns/lawn125.ps;   http://
www.netlib.org/lapack/lawnspdf/lawn125.pdf. UT-CS-97-358, April

1997.

Anderson:1997:PIL

[126] E. Anderson and M. Fahey. Performance improvements to LAPACK for the Cray Scientific Library. LAPACK Working Note 126, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN

37996, USA, April 1997. URL http://www.netlib.org/lapack/lawns/
lawn126.ps;   http://www.netlib.org/lapack/lawnspdf/lawn126.
pdf.

Li:1997:SGE

[127] X. Li. Sparse Gaussian elimination on high performance computers. LAPACK Working Note 127, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, June 1997.

URL http://www.netlib.org/lapack/lawns/lawn127.ps;   http://
www.netlib.org/lapack/lawnspdf/lawn127.pdf. UT-CS-97-368, June

1997.

Petitet:1997:ARM

[128] A. Petitet. Algorithmic redistribution methods for block cyclic decompositions. LAPACK Working Note 128, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, July 1997.

URL http://www.netlib.org/lapack/lawns/lawn128.ps;   http://
www.netlib.org/lapack/lawnspdf/lawn128.pdf. UT-CS-97-371, July

1997. Published in [355].

Choi:1997:NPM

[129] J. Choi. A new parallel matrix multiplication algorithm on distributedmemory concurrent computers. LAPACK Working Note 129, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, September 1997. URL http://www.netlib.

org/lapack/lawns/lawn129.ps;   http://www.netlib.org/lapack/

lawnspdf/lawn129.pdf. UT-CS-97-369, September 1997. Published in

Demmel:1997:ASS

[130] J. Demmel. Accurate SVDs of structured matrices. LAPACK Working Note 130, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, October 1997. URL http://www.

netlib.org/lapack/lawns/lawn130.ps;   http://www.netlib.org/
lapack/lawnspdf/lawn130.pdf. UT-CS-97-375, October 1997.

Whaley:1997:ATL

[131] R. Whaley and J. Dongarra. Automatically tuned linear algebra software. LAPACK Working Note 131, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, December 1997.

URL http://www.netlib.org/lapack/lawns/lawn131.ps;   http://
www.netlib.org/lapack/lawnspdf/lawn131.pdf. UT-CS-97-366, De-

cember 1997. Published in [349].

Tisseur:1998:PDC

[132] F. Tisseur and J. Dongarra. Parallelizing the divide and conquer algorithm for the symmetric tridiagonal eigenvalue problem on distributed memory architectures. LAPACK Working Note 132, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

March 1998. URL http://www.netlib.org/lapack/lawns/lawn132.
ps;   http://www.netlib.org/lapack/lawnspdf/lawn132.pdf. UT-

CS-98-382, March 1998.

Petitet:1998:ARM

[133] A. Petitet and J. Dongarra. Algorithmic redistribution methods for block cyclic distributions. LAPACK Working Note 133, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN

37996, USA, March 1998. URL http://www.netlib.org/lapack/lawns/
lawn133.ps;   http://www.netlib.org/lapack/lawnspdf/lawn133.

pdf. UT-CS-98-383, March 1998. Published in [355].

Wasniewski:1998:HPL

[134] J. Waśniewski and J. Dongarra. High performance linear algebra package — LAPACK90. LAPACK Working Note 134, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

April 1998. URL http://www.netlib.org/lapack/lawns/lawn134.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn134.pdf. UT-CS-98-

384, April 1998. Published in [346].

DAzevedo:1998:PSE

[135] E. D’Azevedo and J. Dongarra. Packed storage extensions for ScaLA-PACK. LAPACK Working Note 135, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, April 1998.

URL http://www.netlib.org/lapack/lawns/lawn135.ps;   http://
www.netlib.org/lapack/lawnspdf/lawn135.pdf. UT-CS-98-385, April

1998.

Blackford:1998:SEP

[136] L. S. Blackford and R. C. Whaley. ScaLAPACK evaluation and performance at the DoD MSRCs. LAPACK Working Note 136, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN

37996, USA, April 1998. URL http://www.netlib.org/lapack/lawns/
lawn136.ps;   http://www.netlib.org/lapack/lawnspdf/lawn136.

pdf. UT-CS-98-388, April 1998.

Blackford:1998:IGD

[137] L. S. Blackford, J. J. Dongarra, C. A. Papadopoulos, and R. C. Whaley. Installation guide and design of the HPF 1.1 interface to ScaLAPACK, SLHPF. LAPACK Working Note 137, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Au-

gust 1998. URL http://www.netlib.org/lapack/lawns/lawn137.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn137.pdf. UT-CS-98-

396, August 1998.

Dongarra:1998:TSL

[138] J. Dongarra, W. Owczarz, J. Waśniewski, and P. Yalamov. Testing software for LAPACK90. LAPACK Working Note 138, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996,

USA, September 1998. URL http://www.netlib.org/lapack/lawns/
lawn138.ps;   http://www.netlib.org/lapack/lawnspdf/lawn138.

pdf. UT-CS-98-401, Sept 1998.

Petitet:1998:NLA

[139] A. Petitet, H. Casanova, J. Dongarra, Y. Robert, and R. C. Whaley. A numerical linear algebra problem solving environment designer’s perspective. LAPACK Working Note 139, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, October 1998.

URL http://www.netlib.org/lapack/lawns/lawn139.ps;   http://
www.netlib.org/lapack/lawnspdf/lawn139.pdf. UT-CS-98-405, Oct

1998. Published in [356, 359].

Casanova:1998:NVD

[140] H. Casanova and J. Dongarra. NetSolve version 1.2: Design and implementation. LAPACK Working Note 140, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Novem-

ber 1998. URL http://www.netlib.org/lapack/lawns/lawn140.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn140.pdf. UT-CS-98-

406, Nov 1998.

Eijkhout:1998:OIL

[141] Victor Eijkhout. Overview of iterative linear system solver packages. LAPACK Working Note 141, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, December 1998.

URL http://www.netlib.org/lapack/lawns/lawn141.ps;   http://
www.netlib.org/lapack/lawnspdf/lawn141.pdf. UT-CS-98-411, Dec

1998.

Arbenz:1999:CPSa

[142] P. Arbenz, A. Cleary, J. Dongarra, and M. Hegland. A comparison of parallel solvers for diagonally dominant and general narrow-banded linear systems. LAPACK Working Note 142, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Febru-

ary 1999. URL http://www.netlib.org/lapack/lawns/lawn142.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn142.pdf. UT-CS-99-

414, Feb 1999. Published in [350].

Arbenz:1999:CPSb

[143] P. Arbenz, A. Cleary, J. Dongarra, and M. Hegland. A comparison of parallel solvers for diagonally dominant and general narrow-banded linear systems II. LAPACK Working Note 143, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

May 1999. URL http://www.netlib.org/lapack/lawns/lawn143.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn143.pdf. UT-CS-99-

415, May 1999.

Eijkhout:1999:EPI

[144] V. Eijkhout. On the existence problem of incomplete factorisation methods. LAPACK Working Note 144, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Decem-

ber 1999. URL http://www.netlib.org/lapack/lawns/lawn144.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn144.pdf. UT-CS-99-

435, Dec 1999.

Eijkhout:1999:WMI

[145] V. Eijkhout. The ‘weighted modification’ incomplete factorisation method. LAPACK Working Note 145, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Decem-

ber 1999. URL http://www.netlib.org/lapack/lawns/lawn145.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn145.pdf. UT-CS-99-

436, Dec 1999.

Andersen:2000:RFC

[146] B. Andersen, F. Gustavson, and J. Waśniewski. A recursive formulation of Cholesky factorization of a matrix in packed storage. LA-PACK Working Note 146, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, May 2000.

URL http://www.netlib.org/lapack/lawns/lawn146.ps;   http://
www.netlib.org/lapack/lawnspdf/lawn146.pdf. UT-CS-00-441, May

2000. Published in [360].

Whaley:2000:AEO

[147] R. C. Whaley, A. Petitet, and J. Dongarra. Automated empirical optimization of software and the ATLAS Project. LAPACK Working Note 147, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, September 2000. URL http://www.netlib.

org/lapack/lawns/lawn147.ps;   http://www.netlib.org/lapack/

lawnspdf/lawn147.pdf. UT-CS-00-448, September 2000. Published in [361].

Bindel:2000:CGR

[148] D. Bindel, J. Demmel, W. Kahan, and O. Marques. On computing Givens rotations reliably and efficiently. LAPACK Working Note 148, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, October 2000. URL http://www.netlib.

org/lapack/lawns/lawn148.ps;   http://www.netlib.org/lapack/

lawnspdf/lawn148.pdf. UT-CS-00-449, October 2000. Published in [362].

Li:2000:DIT

[149] X. Li, J. Demmel, D. Bailey, G. Henry, Y. Hida, J. Iskandar, W. Kahan, A. Kapur, M. Martin, T. Tung, and D. J. Yoo. Design, implementation and testing of extended and mixed precision BLAS. LA-PACK Working Note 149, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, October 2000.

URL http://www.netlib.org/lapack/lawns/lawn149.ps;   http://
www.netlib.org/lapack/lawnspdf/lawn149.pdf. UT-CS-00-451, Octo-

ber 2000. Published in [364].

Anderson:2000:DPR

[150] E. Anderson. Discontinuous plane rotations and the symmetric eigenvalue problem. LAPACK Working Note 150, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Decem-

ber 2000. URL http://www.netlib.org/lapack/lawns/lawn150.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn150.pdf. UT-CS-00-

454, December 2000.

Eijkhout:2001:ADM

[151] V. Eijkhout. Automatic determination of matrix-blocks. LAPACK Working Note 151, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, April 2001. URL http://www.

netlib.org/lapack/lawns/lawn151.ps;   http://www.netlib.org/
lapack/lawnspdf/lawn151.pdf. UT-CS-01-458, April 2001.

Cheng:2001:ILB

[152] S. Cheng and N. Higham. Implementation for LAPACK of a block algorithm for matrix 1-norm estimation. LAPACK Working Note 152, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, August 2001. URL http://www.netlib.

org/lapack/lawns/lawn152.ps;   http://www.netlib.org/lapack/

lawnspdf/lawn152.pdf. UT-CS-01-470, August 2001.

Fahey:2001:NCP

[153] M. Fahey. New complex parallel eigenvalue and eigenvector routines. LAPACK Working Note 153, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, August 2001.

URL http://www.netlib.org/lapack/lawns/lawn153.ps;   http://
www.netlib.org/lapack/lawnspdf/lawn153.pdf. UT-CS-01-471, Au-

gust 2001.

Dhillon:2002:OER

[154] Inderjit S. Dhillon and Beresford N. Parlett. Orthogonal eigenvectors and relative gaps. LAPACK Working Note 154, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Au-

gust 2002. URL http://www.netlib.org/lapack/lawns/lawn154.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn154.pdf. UT-CS-02-

474, August 2002 Published in [366].

Parlett:2002:IDA

[155] Beresford N. Parlett and Osni A. Marques. An implementation of the dqds algorithm positive case. LAPACK Working Note 155, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996,

USA, August 2002. URL http://www.netlib.org/lapack/lawns/
lawn155.ps;   http://www.netlib.org/lapack/lawnspdf/lawn155.

pdf. LBNL-43726, UT-CS-02-475, August 2002. Published in [358].

Eijkhout:2002:PAO

[156] Victor Eijkhout. Polynomial acceleration of optimised multi-grid smoothers basic theory. LAPACK Working Note 156, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996,

USA, August 2002. URL http://www.netlib.org/lapack/lawns/
lawn156.ps;   http://www.netlib.org/lapack/lawnspdf/lawn156.

pdf. UT-CS-02-477, August 2002.

Dongarra:2002:SAN

[157] Jack Dongarra and Victor Eijkhout. Self-adapting numerical software for next generation applications. LAPACK Working Note 157, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, August 2002. URL http://www.netlib.

org/lapack/lawns/lawn157.ps;   http://www.netlib.org/lapack/

lawnspdf/lawn157.pdf. UT-CS-02-484, August 2002 Published in [365].

Anderson:2002:LFE

[158] Edward Anderson. LAPACK3E — A Fortran 90-enhanced version of LA-PACK. LAPACK Working Note 158, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Decem-

ber 2002. URL http://www.netlib.org/lapack/lawns/lawn158.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn158.pdf. UT-CS-02-

497, December 2002.

Dongarra:2003:FCA

[159] Jack Dongarra and Victor Eijkhout. Finite-choice algorithm optimization in Conjugate Gradients. LAPACK Working Note 159, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, January 2003. URL http://www.netlib.

org/lapack/lawns/lawn159.ps;   http://www.netlib.org/lapack/

lawnspdf/lawn159.pdf. UT-CS-03-502, January 2003.

Chen:2003:SAS

[160] Zizhong Chen, Jack Dongarra, Piotr Luszczek, and Kenneth Roche. Self adapting software for numerical linear algebra and LAPACK for clusters. LAPACK Working Note 160, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, January 2003.

URL http://www.netlib.org/lapack/lawns/lawn160.ps;   http://

www.netlib.org/lapack/lawnspdf/lawn160.pdf. UT-CS-03-499, Jan-

uary 2003.

Lucas:2003:LSC

[161] Craig Lucas. LAPack-style codes for level 2 and 3 pivoted Cholesky factorizations. LAPACK Working Note 161, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Jan-

uary 2003. URL http://www.netlib.org/lapack/lawns/lawn161.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn161.pdf. UT-CS-04-

522, February 2004.

Dhillon:2004:DIM

[162] Inderjit S. Dhillon, Beresford N. Parlett, and Christof Vömel. The design and implementation of the MRRR algorithm. LAPACK Working Note 162, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, February 2004. URL http://www.netlib.

org/lapack/lawns/lawn162.ps;   http://www.netlib.org/lapack/

lawnspdf/lawn162.pdf. UT-CS-04-541, December, 2004.

Parlett:2004:HMA

[163] Beresford N. Parlett and Christof Vömel. How the MRRR algorithm can fail on tight eigenvalue clusters. LAPACK Working Note 163, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, December 2004. 15 pp. URL http://www.eecs.berkeley.

edu/Pubs/TechRpts/2004/CSD-04-1367.pdf;   http://www.netlib.
org/lapack/lawns/lawn163.ps;   http://www.netlib.org/lapack/

lawnspdf/lawn163.pdf. UT-CS-04-542, December, 2004.

Demmel:2005:LPR

[164] Jim Demmel and Jack Dongarra. LAPACK 2005 prospectus: Reliable and scalable software for linear algebra computations on high end computers. LAPACK Working Note 164, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Febru-

ary 2005. URL http://www.netlib.org/lapack/lawns/lawn164.ps;
 http://www.netlib.org/lapack/lawnspdf/lawn164.pdf. UT-CS-05-

546, February 2005.

Demmel:2005:EBE

[165] James Demmel, Yozo Hida, W. Kahan, Xiaoye S. Li, Soni Mukherjee, and E. Jason Riedy. Error bounds from extra precise iterative refinement. LAPACK Working Note 165, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Febru-

ary 2005. URL http://www.netlib.org/lapack/lawns/lawn165.ps;

 http://www.netlib.org/lapack/lawnspdf/lawn165.pdf. UT-CS-05-

547, February 2005.

Willems:2005:CBS

[166] Paul R. Willems, Bruno Lang, and Christof Vömel. Computing the bidiagonal SVD using multiple relatively robust representations. LAPACK Working Note 166, Computer Science Division, University of California, Berkeley, Berkeley, CA, USA, August 29, 2005. 20 pp. URL http://www.

netlib.org/lapack/lawnspdf/lawn166.pdf. Also issued as Technical

Report Technical Report UCB//CSD-05-1376.

Marques:2005:SCM

[167] Osni A. Marques, Beresford N. Parlett, and Christof Vömel. Subset computations with the MRRR algorithm. LAPACK Working Note 167, Computer Science Division, University of California, Berkeley, Berkeley, CA,

USA, September 26, 2005. 9 pp. URL http://www.netlib.org/lapack/

lawnspdf/lawn167.pdf. Also issued as Technical Report UCB//CSD-05-1392.

Antonelli:2005:PSP

[168] Dominic Antonelli and Christof Vömel. PDSYEVR. ScaLAPACK’s parallel MRRR algorithm for the symmetric eigenvalue problem. LAPACK Working Note 168, Computer Science Division, University of California, Berkeley, Berkeley, CA, USA, August 29, 2005. 18 pp. URL http://www.

netlib.org/lapack/lawnspdf/lawn168.pdf. Also issued as Technical

Report UCB//CSD-05-1399.

Drmac:2005:NFA

[169] Zlatko Drmač and Krešimir Veselić. New fast and accurate Jacobi SVD algorithm: I. LAPACK Working Note 169, Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia., August 30,

2005. 39 pp. URL http://www.netlib.org/lapack/lawnspdf/lawn169.
pdf.

Drmac:2005:NFAb

[170] Zlatko Drmač and Krešimir Veselić. New fast and accurate Jacobi SVD algorithm: II. LAPACK Working Note 170, Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia., August 30,

2005. 25 pp. URL http://www.netlib.org/lapack/lawnspdf/lawn170.
pdf.

Kressner:2006:BAR

[171] Daniel Kressner. Block algorithms for reordering standard and generalized Schur forms. LAPACK Working Note 171, Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia., February 17,

2006. 11 pp. URL http://www.netlib.org/lapack/lawnspdf/lawn171.
pdf.

Marques:2005:BIF

[172] Osni A. Marques, E. Jason Riedy, and Christof Vömel. Benefits of IEEE-754 features in modern symmetric tridiagonal eigensolvers. LAPACK Working Note 172, Computer Science Division, University of California, Berkeley, Berkeley, CA, USA, September 30, 2005. 22 pp. URL http://

www.netlib.org/lapack/lawnspdf/lawn172.pdf. Also issued as Tech-

nical Report UCB//CSD-05-1414.

Kaagstrom:2006:MVQ

[173] Bo Kågström and Daniel Kressner. Multishift variants of the QZ algorithm with aggressive early deflation. LAPACK Working Note 173, Department of Computing Science, Umeå University, Umeå, Sweden, Febru-

ary 20, 2006. 42 pp. URL http://www.netlib.org/lapack/lawnspdf/

lawn173.pdf. Also appeared as technical report UMINF-05.11.

Howell:2005:CEB

[174] G. W. Howell, J. W. Demmel, C. T. Fulton, S. Hammarling, and K. Marmol. Cache efficient bidiagonalization using BLAS 2.5 operators. LA-PACK Working Note 174, North Carolina State University; University of California, Berkeley; Florida Institute of Technology; Numerical Algorithms Group; Harris Corporation, Raleigh, NC 27697, USA; Berkeley, CA 94720, USA; Melbourne, FL 32901, USA; Oxford, UK; Melbourne, FL 32901, November 1, 2005. 39 pp. URL http://www.netlib.org/

lapack/lawnspdf/lawn174.pdf.

Langou:2006:EPB

[175] Julie Langou, Julien Langou, Piotr Luszczek, Jakub Kurzak, Alfredo Buttari, and Jack Dongarra. Exploiting the performance of 32 bit floating point arithmetic in obtaining 64 bit accuracy (revisiting iterative refinement for linear systems). LAPACK Working Note 175, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, June 2006. 17 pp. URL http://www.netlib.org/

lapack/lawnspdf/lawn175.pdf;   http://www.netlib.org/lapack/
lawnspdf/lawn175.ps.

Drmac:2006:FRR

[176] Zlatko Drmač and Zvonimir Bujanović. On the failure of rank revealing QR factorization software — a case study. LAPACK Working Note 176, Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia, June 2, 2006. 27 pp. URL http://www.netlib.org/

lapack/lawnspdf/lawn176.pdf;   http://www.netlib.org/lapack/
lawnspdf/lawn176.ps.

Kurzak:2006:IMP

[177] Jakub Kurzak and Jack Dongarra. Implementation of the mixed-precision high performance LINPACK benchmark on the CELL Processor. LA-PACK Working Note 177, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, September 2006. 12

pp. URL http://www.netlib.org/lapack/lawnspdf/lawn177.pdf;
http://www.netlib.org/lapack/lawnspdf/lawn177.ps. Also available

as UT-CS-06-580.

Kurzak:2006:ILA

[178] Jakub Kurzak and Jack Dongarra. Implementing linear algebra routines on multi-core processors with pipelining and a look ahead. LA-PACK Working Note 178, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, September 2006. 11

pp. URL http://www.netlib.org/lapack/lawnspdf/lawn178.pdf;
http://www.netlib.org/lapack/lawnspdf/lawn178.ps. Also available

as UT-CS-06-581.

Baboulin:2006:PTS

[179] Marc Baboulin, Luc Giraud, Serge Gratton, and Julien Langou. Parallel tools for solving incremental dense least squares problems. application to space geodesy. LAPACK Working Note 179, CERFACS, 42 avenue Gaspard Coriolis, 31057 Toulouse Cedex, France, September

2006. URL http://www.netlib.org/lapack/lawnspdf/lawn179.pdf;
 http://www.netlib.org/lapack/lawnspdf/lawn179.ps. Also avail-

able as UT-CS-06-582.

Buttari:2006:UMP

[180] Alfredo Buttari, Jack J. Dongarra, Jakub Kurzak, Piotr Luszczek, and Stanimire Tomov. Using mixed precision for sparse matrix computations to enhance the performance while achieving 64-bit accuracy. LA-PACK Working Note 180, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, October 22,

2006. URL http://www.netlib.org/lapack/lawnspdf/lawn180.pdf.

UT-CS-06-584.

Demmel:2007:PNL

[181] James W. Demmel, Jack J. Dongarra, Beresford N. Parlett, William Kahan, Ming Gu, David S. Bindel, Yozo Hida, Xiaoye S. Li, Osni A. Marques, E. Jason Riedy, Christof Vömel, Julien Langou, Piotr Luszczek, Jakub Kurzak, Alfredo Buttari, Julie Langou, and Stanimire Tomov. Prospectus for the next LAPACK and ScaLAPACK libraries. LAPACK Working Note 181, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, March 11, 2007. URL http://

www.netlib.org/lapack/lawnspdf/lawn181.pdf. UT-CS-07-592.

Demmel:2007:TIL

[182] James W. Demmel, Osni A. Marques, Beresford N. Parlett, and Christof Vömel. A testing infrastructure for LAPACK’s symmetric eigensolvers. LAPACK Working Note 182, Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA, USA,

April 2007. URL http://www.netlib.org/lapack/lawnspdf/lawn182.
pdf.

Demmel:2007:PAL

[183] James W. Demmel, Osni A. Marques, Beresford N. Parlett, and Christof Vömel. Performance and accuracy of LAPACK’s symmetric tridiagonal eigensolvers. LAPACK Working Note 183, Department of Electrical Engineering and Computer Science, University of California, Berkeley,

Berkeley, CA, USA, April 2007. URL http://www.netlib.org/lapack/
lawnspdf/lawn183.pdf.

Kurzak:2007:SSL

[184] Jakub Kurzak, Alfredo Buttari, and Jack J. Dongarra. Solving systems of linear equations on the CELL processor using Cholesky factorization. LA-PACK Working Note 184, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, May 2007. URL http:

//www.netlib.org/lapack/lawnspdf/lawn184.pdf. UT-CS-07-596.

Buttari:2007:LPH

[185] Alfredo Buttari, Jack J. Dongarra, and Jakub Kurzak. Limitations of the PlayStation 3 for high performance cluster computing. LAPACK Working Note 185, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, May 2007. URL http://www.

netlib.org/lapack/lawnspdf/lawn185.pdf. UT-CS-07-597.

Demmel:2007:FLAa

[186] James W. Demmel, Ioana Dumitriu, and Olga Holtz. Fast linear algebra is stable. LAPACK Working Note 186, Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA,

USA, May 18, 2007. URL http://www.netlib.org/lapack/lawnspdf/

lawn186.pdf. Published in [367].

Byers:2007:LXT

[187] Ralph Byers. LAPACK 3.1 xHSEQR: Tuning and implementation notes on the small bulge multi-shift QR algorithm with aggressive early deflation. LAPACK Working Note 187, Department of Mathematics, University of Kansas, Lawrence, Kansas 66045, USA, May 2007. URL http://

www.netlib.org/lapack/lawnspdf/lawn187.pdf.

Demmel:2007:EPI

[188] James W. Demmel, Yozo Hida, Xiaoye S. Li, and E. Jason Riedy. Extra-precise iterative refinement for overdetermined least squares problems. LAPACK Working Note 188, Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA,

USA, May 30, 2007. URL http://www.netlib.org/lapack/lawnspdf/

lawn188.pdf. Published in [369].

Alvaro:2008:FSS

[189] Wesley Alvaro, Jakub Kurzak, and Jack J. Dongarra. Fast and small short vector SIMD matrix multiplication kernels for the CELL processor. LAPACK Working Note 189, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, January

2008. URL http://www.netlib.org/lapack/lawnspdf/lawn189.pdf.

UT-CS-08-609.

Buttari:2007:PTQ

[190] Alfredo Buttari, Julien Langou, Jakub Kurzak, and Jack J. Dongarra. Parallel tiled QR factorization for multicore architectures. LAPACK Working Note 190, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, July 2007. URL http://www.

netlib.org/lapack/lawnspdf/lawn190.pdf. UT-CS-07-598. Published

in [368].

Buttari:2007:CPT

[191] Alfredo Buttari, Julien Langou, Jakub Kurzak, and Jack J. Dongarra. A class of parallel tiled linear algebra algorithms for multicore architectures. LAPACK Working Note 191, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Septem-

ber 2007. URL http://www.netlib.org/lapack/lawnspdf/lawn191.

pdf. UT-CS-07-600.

Granat:2007:PER

[192] Robert Granat, Bo Kågström, and Daniel Kressner. Parallel eigenvalue reordering in real Schur forms. LAPACK Working Note 192, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN

37996, USA, September 2007. URL http://www.netlib.org/lapack/
lawnspdf/lawn192.pdf.

Baboulin:2007:CCC

[193] Marc Baboulin, Jack J. Dongarra, Serge Gratton, and Julien Langou. Computing the conditioning of the components of a linear least squares solution. LAPACK Working Note 193, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Septem-

ber 2007. URL http://www.netlib.org/lapack/lawnspdf/lawn193.

pdf. UT-CS-07-604.

Vomel:2007:RRT

[194] Christof Vömel. A refined representation tree for MRRR. LAPACK Working Note 194, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, November 2007. URL http://

www.netlib.org/lapack/lawnspdf/lawn194.pdf.

Vomel:2007:SMA

[195] Christof Vömel. ScaLAPACK’s MRRR algorithm. LAPACK Working Note 195, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, November 2007. URL http://

www.netlib.org/lapack/lawnspdf/lawn195.pdf.

Drmac:2007:GCP

[196] Zlatko Drmač. A global convergence proof of cyclic Jacobi methods with block rotations. LAPACK Working Note 196, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

December 10, 2007. URL http://www.netlib.org/lapack/lawnspdf/
lawn196.pdf.

Volkov:2008:UGA

[197] Vasily Volkov and James W. Demmel. Using GPUs to accelerate the bisection algorithm for finding eigenvalues of symmetric tridiagonal matrices. LAPACK Working Note 197, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, January 2008.

URL http://www.netlib.org/lapack/lawnspdf/lawn197.pdf.

Kaagstrom:2008:BAR

[198] Bo Kågström, Daniel Kressner, Enrique S. Quintana-Orti, and Gregorio Quintana-Orti. Blocked algorithms for the reduction to Hessenbergtriangular form revisited. LAPACK Working Note 198, Department of Computing Science and HPC2N, Umeå University, S-901 Umeå, Swe-

den, February 2008. URL http://www.netlib.org/lapack/lawnspdf/
lawn198.pdf.

Gustavson:2008:RFP

[199] Fred G. Gustavson, Jerzy Wasniewski, Jack J. Dongarra, and Julien Langou. Rectangular full packed format for Cholesky’s algorithm: Factorization, solution and inversion. LAPACK Working Note 199, Department of Computer Science, University of Tennessee, Knoxville, Knoxville,

TN 37996, USA, April 2008. URL http://www.netlib.org/lapack/
lawnspdf/lawn199.pdf. UT-CS-08-614.

Baboulin:2008:SID

[200] Marc Baboulin, Jack J. Dongarra, and Stanimire Tomov. Some issues in dense linear algebra for multicore and special purpose architectures. LA-PACK Working Note 200, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, May 2008. URL http:

//www.netlib.org/lapack/lawnspdf/lawn200.pdf. UT-CS-08-615.

Kurzak:2008:QFC

[201] Jakub Kurzak and Jack J. Dongarra. QR factorization for the CELL processor. LAPACK Working Note 201, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

May 2008. URL http://www.netlib.org/lapack/lawnspdf/lawn201.

pdf. UT-CS-08-616.

Volkov:2008:LQC

[202] Vasily Volkov and James W. Demmel. LU, QR and Cholesky factorizations using vector capabilities of GPUs. LAPACK Working Note 202, Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA, USA, May 2008. URL http://www.

netlib.org/lapack/lawnspdf/lawn202.pdf.

Demmel:2008:NND

[203] James W. Demmel, Yozo Hida, Mark F. Hoemmen, and E. Jason Riedy. Non-negative diagonals and high performance on low-profile matrices from householder QR. LAPACK Working Note 203, Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA, USA, May 30, 2008. URL http://www.netlib.org/

lapack/lawnspdf/lawn203.pdf.

Demmel:2008:COP

[204] James W. Demmel, Laura Grigori, Mark F. Hoemmen, and Julien Langou. Communication-optimal parallel and sequential QR and LU factorizations. LAPACK Working Note 204, Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA, USA, August 2008. URL http://www.eecs.

berkeley.edu/Pubs/TechRpts/2008/EECS-2008-89.html;   http://
www.netlib.org/lapack/lawnspdf/lawn204.pdf.

Bosilca:2008:ABF

[205] George Bosilca, Remi Delmas, Jack J. Dongarra, and Julien Langou. Algorithmic based fault tolerance applied to high performance computing. LAPACK Working Note 205, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, May 23,

2008. URL http://www.netlib.org/lapack/lawnspdf/lawn205.pdf.

UT-CS-08-620.

Dongarra:2008:PLB

[206] Jack J. Dongarra and Julien Langou. The problem with the Linpack benchmark matrix generator. LAPACK Working Note 206, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN

37996, USA, June 12, 2008. URL http://www.netlib.org/lapack/

lawnspdf/lawn206.pdf. Version 1; version 2 is dated 18 September 2008.

Baboulin:2008:UDT

[207] Marc Baboulin and Serge Gratton. Using dual techniques to derive componentwise and mixed condition numbers for a linear functional of a linear least squares solution. LAPACK Working Note 207, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996,

USA, August 2008. URL http://www.netlib.org/lapack/lawnspdf/

lawn207.pdf. UT-CS-08-622.

Ltaief:2008:PBH

[208] Hatem Ltaief, Jakub Kurzak, and Jack Dongarra. Parallel block Hessenberg reduction using algorithms-by-tiles for multicore architectures revisited. LAPACK Working Note 208, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, August

2008. URL http://www.netlib.org/lapack/lawnspdf/lawn208.pdf.

UT-CS-08-624.

Ltaief:2008:PBT

[209] Hatem Ltaief, Jakub Kurzak, and Jack Dongarra. Parallel band two-sided matrix bidiagonalization for multicore architectures. LAPACK Working Note 209, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, October 2008. URL http://www.

netlib.org/lapack/lawnspdf/lawn209.pdf. UT-CS-08-631.

Tomov:2008:TDL

[210] Stanimire Tomov, Jack Dongarra, and Marc Baboulin. Towards dense linear algebra for hybrid GPU accelerated manycore systems. LAPACK Working Note 210, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, October 2008. URL http:

//www.netlib.org/lapack/lawnspdf/lawn210.pdf. UT-CS-08-632.

Gustavson:2008:LCK

[211] Fred G. Gustavson, Jerzy Wasniewski, and Jack Dongarra. Level-3 Cholesky kernel subroutine of a fully portable high performance minimal storage hybrid format Cholesky algorithm. LAPACK Working Note 211, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, December 2008. URL http://www.netlib.

org/lapack/lawnspdf/lawn211.pdf. UT-CS-08-634.

Li:2009:NAT

[212] Yinan Li, Jack Dongarra, and Stanimire Tomov. A note on auto-tuning GEMM for GPUs. LAPACK Working Note 212, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996,

USA, January 2009. URL http://www.netlib.org/lapack/lawnspdf/

lawn212.pdf. UT-CS-09-635.

Kurzak:2009:SLA

[213] Jakub Kurzak, Hatem Ltaief, Jack Dongarra, and Rosa M. Badia. Scheduling linear algebra operations on multicore processors. LAPACK Working Note 213, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, February 2009. URL http:

//www.netlib.org/lapack/lawnspdf/lawn213.pdf. UT-CS-09-636.

Kurzak:2009:STS

[214] Jakub Kurzak, Hatem Ltaief, and Jack Dongarra. Scheduling two-sided transformations using algorithms-by-tiles on multicore architectures. LA-PACK Working Note 214, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, February 2009. URL

http://www.netlib.org/lapack/lawnspdf/lawn214.pdf. UT-CS-09-

Ballard:2009:COP

[215] Grey Ballard, James Demmel, Olga Holtz, and Oded Schwartz. Communication-optimal parallel and sequential Cholesky decomposition. LAPACK Working Note 215, Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA, USA,

February 13, 2009. URL http://www.netlib.org/lapack/lawnspdf/
lawn215.pdf.

Granat:2009:NPQ

[216] Robert Granat, Bo Kågström, and Daniel Kressner. A novel parallel QR algorithm for hybrid distributed memory HPC systems. LAPACK Working Note 216, Department of Computing Science and HPC2N, Umeå University, S-901 Umeå, Sweden, April 2009. URL http://www.netlib.

org/lapack/lawnspdf/lawn216.pdf. UMINF-09.06.

Agullo:2009:CSO

[217] Emmanuel Agullo, Bilel Hadri, Hatem Ltaief, and Jack Dongarra. Comparative study of one-sided factorizations with multiple software packages on multi-core hardware. LAPACK Working Note 217, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN

37996, USA, April 28, 2009. URL http://www.netlib.org/lapack/
lawnspdf/lawn217.pdf. UT-CS-09-640.

Ballard:2009:MCL

[218] Grey Ballard, James Demmel, Olga Holtz, and Oded Schwartz. Minimizing communication in linear algebra. LAPACK Working Note 218, Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA, USA, May 15, 2009. URL http://

www.netlib.org/lapack/lawnspdf/lawn218.pdf. UCB/EECS-2009-62.

Tomov:2009:ARU

[219] Stanimire Tomov and Jack Dongarra. Accelerating the reduction to upper Hessenberg form through hybrid GPU-based computing. LAPACK Working Note 219, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, May 24, 2009. URL http://www.

netlib.org/lapack/lawnspdf/lawn219.pdf. UT-CS-09-642.

Kurzak:2009:FDS

[220] Jakub Kurzak and Jack Dongarra. Fully dynamic scheduler for numerical computing on multicore processors. LAPACK Working Note 220, Department of Computer Science, University of Tennessee, Knoxville, Knoxville,

TN 37996, USA, June 4, 2009. URL http://www.netlib.org/lapack/
lawnspdf/lawn220.pdf. UT-CS-09-643.

Song:2009:DTS

[221] Fengguang Song, Asim YarKhan, and Jack Dongarra. Dynamic task scheduling for linear algebra algorithms on distributed-memory multicore systems. LAPACK Working Note 221, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, April 13,

2009. URL http://www.netlib.org/lapack/lawnspdf/lawn221.pdf.

UT-CS-09-638.

Hadri:2009:EPT

[222] Bilel Hadri, Hatem Ltaief, Emmanuel Agullo, and Jack Dongarra. Enhancing parallelism of tile QR factorization for multicore architectures. LAPACK Working Note 222, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, September 4,

2009. URL http://www.netlib.org/lapack/lawnspdf/lawn222.pdf.

UT-CS-09-645.

Ltaief:2009:SHP

[223] Hatem Ltaief, Stanimire Tomov, Rajib Nath, Peng Du, and Jack Dongarra. A scalable high performant Cholesky factorization for multicore with GPU accelerators. LAPACK Working Note 223, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN

37996, USA, November 25, 2009. URL http://www.netlib.org/lapack/
lawnspdf/lawn223.pdf. UT-CS-09-646.

Agullo:2010:QFT

[224] Emmanuel Agullo, Camille Coti, Jack Dongarra, Thomas Herault, and Julien Langou. QR factorization of tall and skinny matrices in a grid computing environment. LAPACK Working Note 224, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996,

USA, April 6, 2010. URL http://www.netlib.org/lapack/lawnspdf/

lawn224.pdf. UT-CS-10-651. Published in the Proceedings of IPDPS 2010: 24th IEEE International Parallel and Distributed Processing Symposium Atlanta GA April 2010.

Tomov:2010:DLA

[225] Stanimire Tomov, Rajib Nath, Hatem Ltaief, and Jack Dongarra. Dense linear algebra solvers for multicore with GPU accelerators. LAPACK Working Note 225, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, April 18, 2010. URL

http://www.netlib.org/lapack/lawnspdf/lawn225.pdf. UT-CS-09-

649. Published in the Proceedings of IPDPS 2010: 24th IEEE International Parallel and Distributed Processing Symposium Atlanta GA April 2010.

Grigori:2010:CCO

[226] Laura Grigori, James W. Demmel, and Hua Xiang. CALU: a communication optimal LU factorization algorithm. LAPACK Working Note 226, Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA, USA, March 15, 2010. URL

http://www.netlib.org/lapack/lawnspdf/lawn226.pdf. UCB/EECS-

2010-29. Submitted to SIAM Journal on Matrix Analysis and Applications (SIMAX).

Nath:2010:IMG

[227] Rajib Nath, Stanimire Tomov, and Jack Dongarra. An improved MAGMA GEMM for Fermi GPUs. LAPACK Working Note 227, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN

37996, USA, July 29, 2010. URL http://www.netlib.org/lapack/
lawnspdf/lawn227.pdf. UT-CS-10-655.

Du:2010:COT

[228] Peng Du, Rick Weber, Piotr Luszczek, Stanimire Tomov, Gregory Peterson, and Jack Dongarra. From CUDA to OpenCL: Towards a performance-portable solution for multi-platform GPU programming. LA-PACK Working Note 228, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, September 6,

2010. URL http://www.netlib.org/lapack/lawnspdf/lawn228.pdf.

UT-CS-10-656.

Kurzak:2010:ITF

[229] Jakub Kurzak, Rajib Nath, Peng Du, and Jack Dongarra. An implementation of the tile QR factorization for a GPU and multiple CPUs. LAPACK Working Note 229, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, September 15,

2010. URL http://www.netlib.org/lapack/lawnspdf/lawn229.pdf.

UT-CS-10-657. Submitted to PARA’10.

Agullo:2010:FCB

[230] Emmanuel Agullo, Cedric Augonnet, Jack Dongarra, Hatem Ltaief, Raymond Namyst, Samuel Thibault, and Stanimire Tomov. Faster, cheaper, better — a hybridization methodology to develop linear algebra software for GPUs. LAPACK Working Note 230, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

September 15, 2010. URL http://www.netlib.org/lapack/lawnspdf/

lawn230.pdf. UT-CS-10-658. To appear in GPU Computing GEMs, vol. 2.

Bosilca:2010:DGD

[231] G. Bosilca, A. Bouteiller, A. Danalis, T. Herault, P. Lemarinier, and J. Dongarra. DAGuE: A generic distributed DAG engine for high performance computing. LAPACK Working Note 231, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

September 15, 2010. URL http://www.netlib.org/lapack/lawnspdf/

lawn231.pdf. UT-CS-10-659.

Bosilca:2010:DMT

[232] G. Bosilca, A. Bouteiller, A. Danalis, M. Faverge, H. Haidar, T. Herault, J. Kurzak, J. Langou, P. Lemarinier, H. Ltaief, P. Luszczekl, A. YarKhan, and J. Dongarra. Distributed-memory task execution and dependence tracking within DAGuE and the DPLASMA Project. LAPACK Working Note 232, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, September 15, 2010. URL http:/

/www.netlib.org/lapack/lawnspdf/lawn232.pdf. UT-CS-10-660.

Agullo:2010:FMN

[233] E. Agullo, C. Augonnet, J. Dongarra, M. Faverge, H. Ltaief, S. Thibault, and S. Tomov. QR factorization on a multicore node enhanced with multiple GPU accelerators. LAPACK Working Note 233, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996,

USA, October 2010. URL http://www.netlib.org/lapack/lawnspdf/

lawn233.pdf. UT-CS-10-XXX, published in Proceedings of IPDPS 2011.

Dongarra:2010:RTT

[234] Jack Dongarra and Piotr Luszczek. Reducing the time to tune parallel dense linear algebra routines with partial execution and performance modelling. LAPACK Working Note 235, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, October

8, 2010. URL http://www.netlib.org/lapack/lawnspdf/lawn235.pdf.

UT-CS-10-661.

Baboulin:2010:CCT

[235] Marc Baboulin and Serge Gratton. A contribution to the conditioning of the total least squares problem. LAPACK Working Note 236, INRIA (Institut National de Recherche en Informatique et en Automatique), Rocquencourt, France, November 5, 2010. URL http://www.netlib.org/

lapack/lawnspdf/lawn236.pdf. INRIA report.

Ballard:2010:MCE

[236] Grey Ballard, James Demmel, and Ioana Dumitriu. Minimizing communication for eigenproblems and the singular value decomposition. LAPACK Working Note 237, Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA, USA, November

13, 2010. URL http://www.netlib.org/lapack/lawnspdf/lawn237.

pdf. UCB/EECS-2010-136.

Solomonik:2011:COPa

[237] Edgar Solomonik and James Demmel. Communication-optimal parallel 2.5D matrix multiplication and LU factorization algorithms. LAPACK Working Note 238, Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA, USA, February

9, 2011. URL http://www.netlib.org/lapack/lawnspdf/lawn238.pdf.

UCB/EECS-2011-10.

Ballard:2011:CBH

[238] Grey Ballard, James Demmel, and Andrew Gearhart. Communication bounds for heterogeneous architectures. LAPACK Working Note 239, Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA, USA, February 11, 2011. URL http:

//www.netlib.org/lapack/lawnspdf/lawn239.pdf. UCB/EECS-2011-

13.

Anderson:2011:CAD

[239] Michael Anderson, Grey Ballard, James Demmel, and Kurt Keutzer. Communication-avoiding QR decomposition for GPUs. LAPACK Working Note 240, Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA, USA, February 18,

2011. URL http://www.netlib.org/lapack/lawnspdf/lawn240.pdf.

Update of UCB/EECS-2010-131. To appear in IPDPS’11.

Song:2011:STC

[240] Fengguang Song, Hatem Ltaief, Bilel Hadri, and Jack Dongarra. Scalable tile communication-avoiding QR factorization on multicore cluster systems. LAPACK Working Note 241, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, March

4, 2011. URL http://www.netlib.org/lapack/lawnspdf/lawn241.pdf.

UT-CS-10-653. Published at SC’10.

Agullo:2011:FEA

[241] Emmanuel Agullo, Jack Dongarra, Rajib Nath, and Stanimire Tomov. A fully empirical autotuned dense QR factorization for multicore architectures. LAPACK Working Note 242, INRIA (Institut National de Recherche en Informatique et en Automatique), Rocquen-

court, France, March 9, 2011. URL http://www.netlib.org/lapack/
lawnspdf/lawn242.pdf. INRIA-7526.

Haidar:2011:ADS

[242] Azzam Haidar, Hatem Ltaief, Asim YarKhan, and Jack Dongarra. Analysis of dynamically scheduled tile algorithms for dense linear algebra on multicore architectures. LAPACK Working Note 243, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN

37996, USA, March 10, 2011. URL http://www.netlib.org/lapack/

lawnspdf/lawn243.pdf. UT-CS-11-666. Submitted at Concurrency and Computations.

Luszczek:2011:TST

[243] Piotr Luszczek, Hatem Ltaief, and Jack Dongarra. Two-stage tridiagonal reduction for dense symmetric matrices using tile algorithms on multicore architectures. LAPACK Working Note 244, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996,

USA, April 18, 2011. URL http://www.netlib.org/lapack/lawnspdf/

lawn244.pdf. UT-CS-11-670.

Kurzak:2011:AGF

[244] Jakub Kurzak, Stanimire Tomov, and Jack Dongarra. Autotuning GEMMs for Fermi. LAPACK Working Note 245, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996,

USA, April 18, 2011. URL http://www.netlib.org/lapack/lawnspdf/

lawn245.pdf. UT-CS-11-671. Submitted at SC11 November 12-18, 2011, Seattle, Washington, USA.

Baboulin:2011:ALS

[245] Marc Baboulin, Jack Dongarra, Julien Herrmann, and Stanimire Tomov. Accelerating linear system solutions using randomization techniques. LA-PACK Working Note 246, INRIA (Institut National de Recherche en Informatique et en Automatique), Rocquencourt, France, May 15, 2011.

URL http://www.netlib.org/lapack/lawnspdf/lawn246.pdf. INRIA

RR-7616.

Ltaief:2011:HPB

[246] Hatem Ltaief, Piotr Luszczek, and Jack Dongarra. High performance bidiagonal reduction using tile algorithms on homogeneous multicore architectures. LAPACK Working Note 247, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, May 18,

2011. URL http://www.netlib.org/lapack/lawnspdf/lawn247.pdf.

UT-CS-11-673. Submitted at TOMS.

Solomonik:2011:COPb

[247] Edgar Solomonik and James Demmel. Communication-optimal parallel 2.5D matrix multiplication and LU factorization algorithms. LAPACK Working Note 248, Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA, USA, June 7,

2011. URL http://www.netlib.org/lapack/lawnspdf/lawn248.pdf.

UCB/EECS-2011-72.

Gustavson:2011:LCF

[248] Fred G. Gustavson, Jerzy Wásniewski, Jack J. Dongarra, José R. Herrero, and Julien Langou. Level-3 Cholesky factorization routines as part of many Cholesky algorithms. LAPACK Working Note 249, ????, ????,

2011. URL http://www.netlib.org/lapack/lawnspdf/lawn249.pdf.

DTU/IMM-Technical-Report-2011-11, submitted at TOMS.

Song:2011:ESM

[249] Fengguang Song, Stanimire Tomov, and Jack Dongarra. Efficient support for matrix computations on heterogeneous multi-core and multi-GPU architectures. LAPACK Working Note 250, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996,

USA, June 16, 2011. URL http://www.netlib.org/lapack/lawnspdf/

lawn250.pdf. UT-CS-11-668.

Ltaief:2011:PHP

[250] Hatem Ltaief, Piotr Luszczek, and Jack Dongarra. Profiling high performance dense linear algebra algorithms on multicore architectures for power and energy efficiency. LAPACK Working Note 251, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996,

USA, June 21, 2011. URL http://www.netlib.org/lapack/lawnspdf/

lawn251.pdf. UT-CS-11-674.

Du:2011:SER

[251] Peng Du, Piotr Luszczek, Stanimire Tomov, and Jack Dongarra. Soft error resilient QR factorization for hybrid system. LAPACK Working Note 252, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, July 1, 2011. URL http://www.netlib.org/

lapack/lawnspdf/lawn252.pdf. UT-CS-11-675.

Du:2011:ABF

[252] Peng Du, Aurelien Bouteiller, George Bosilca, Thomas Herault, and Jack Dongarra. Algorithm-based fault tolerance for dense matrix factorizations. LAPACK Working Note 253, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, August

5, 2011. URL http://www.netlib.org/lapack/lawnspdf/lawn253.pdf.

UT-CS-11-676.

Haidar:2011:PRC

[253] Azzam Haidar, Hatem Ltaief, and Jack Dongarra. Parallel reduction to condensed forms for symmetric eigenvalue problems using aggregated finegrained and memory-aware kernels. LAPACK Working Note 254, Department of Computer Science, University of Tennessee, Knoxville, Knoxville,

TN 37996, USA, August 5, 2011. URL http://www.netlib.org/lapack/

lawnspdf/lawn254.pdf. UT-CS-11-677 Aug 5 2011.

Solomonik:2011:ICP

[254] Edgar Solomonik, Abhinav Bhatele, and James Demmel. Improving communication performance in dense linear algebra via topology aware collectives. LAPACK Working Note 255, Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berke-

ley, CA, USA, August 15, 2011. URL http://www.netlib.org/lapack/
lawnspdf/lawn255.pdf. UCB/EECS-2011-92.

Du:2011:HPL

[255] Peng Du, Piotr Luszczek, and Jack Dongarra. High performance linear system solver with resilience to multiple soft errors. LAPACK Working Note 256, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, October 2011. URL http://www.

netlib.org/lapack/lawnspdf/lawn256.pdf. UT-CS-11-683.

Dongarra:2011:HFA

[256] Jack Dongarra, Mathieu Faverge, Thomas Herault, Julien Langou, and Yves Robert. Hierarchical QR factorization algorithms for multi-core cluster systems. LAPACK Working Note 257, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Oc-

tober 2011. URL http://www.netlib.org/lapack/lawnspdf/lawn257.

pdf. UT-CS-11-684.

Anzt:2011:BAR

[257] Hartwig Anzt, Stanimire Tomov, Jack Dongarra, and Vincent Heuveline. A block-asynchronous relaxation method for graphics processing units.

LAPACK Working Note 258, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, December

2011. URL http://www.netlib.org/lapack/lawnspdf/lawn258.pdf.

UT-CS-11-687.

Dongarra:2011:ANA

[258] Jack Dongarra, Mathieu Faverge, Hatem Ltaief, and Piotr Luszczek. Achieving numerical accuracy and high performance using recursive tile LU factorization. LAPACK Working Note 259, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996,

USA, December 2011. URL http://www.netlib.org/lapack/lawnspdf/

lawn259.pdf. UT-CS-11-688.

Anzt:2011:GAA

[259] Hartwig Anzt, Piotr Luszczek, Jack Dongarra, and Vincent Heuveline. GPU-accelerated asynchronous error correction for mixed precision iterative refinement. LAPACK Working Note 260, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996,

USA, December 2011. URL http://www.netlib.org/lapack/lawnspdf/

lawn260.pdf. UT-CS-11-690.

Baboulin:2011:PTS

[260] Marc Baboulin, Dulceneia Becker, and Jack Dongarra. A parallel tiled solver for dense symmetric indefinite systems on multicore architectures. LAPACK Working Note 261, INRIA (Institut National de Recherche en Informatique et en Automatique), Rocquencourt, France, December 2011.

URL http://www.netlib.org/lapack/lawnspdf/lawn261.pdf. INRIA-

7762.

Bougeret:2011:URR

[261] Marin Bougeret, Henri Casanova, Yves Robert, Frédéric Vivien, and Dounia Zaidouni. Using replication for resilience on exascale systems. LAPACK Working Note 262, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, December

2011. URL http://www.netlib.org/lapack/lawnspdf/lawn262.pdf.

UT-CS-11-691.

Khabou:2012:FPR

[262] Amal Khabou, James W. Demmel, Laura Grigori, and Ming Gu. LU factorization with panel rank revealing pivoting and its communication avoiding version. LAPACK Working Note 263, Department of Electrical Engineering and Computer Science, University of California, Berkeley, Berkeley, CA, USA, January 2012. URL http://www.netlib.org/

lapack/lawnspdf/lawn263.pdf. UCB/EECS-2012-XX.

Bosilca:2012:DLA

[263] George Bosilca, Aurelien Bouteiller, Anthony Danalis, Thomas Herault, Piotr Luszczek, and Jack J. Dongarra. Dense linear algebra on distributed heterogeneous hardware with a symbolic DAG approach. LAPACK Working Note 264, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, January 2012. URL http://www.

netlib.org/lapack/lawnspdf/lawn264.pdf.

Bougeret:2012:UGR

[264] Marin Bougeret, Henri Casanova, Yves Robert, Frédéric Vivien, and Dounia Zaidouni. Using group replication for resilience on exascale systems. LAPACK Working Note 265, INRIA (Institut National de Recherche en Informatique et en Automatique), Rocquencourt, France, March 2012.

URL http://www.netlib.org/lapack/lawnspdf/lawn265.pdf.

Kurzak:2012:FPP

[265] Jakub Kurzak, Piotr Luszczek, Mathieu Faverge, and Jack Dongarra. LU factorization with partial pivoting for a multi-CPU, multi-GPU shared memory system. LAPACK Working Note 266, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

April 2012. URL http://www.netlib.org/lapack/lawnspdf/lawn266.
pdf.

Kurzak:2012:PRA

[266] Jakub Kurzak, Piotr Luszczek, Stanimire Tomov, and Jack Dongarra. Preliminary results of autotuning GEMM kernels for the NVIDIA Kepler Architecture GeForce GTX 680. LAPACK Working Note 267, Department of Computer Science, University of Tennessee, Knoxville, Knoxville,

TN 37996, USA, April 2012. URL http://www.netlib.org/lapack/
lawnspdf/lawn267.pdf.

Robert:2012:CPR

[267] Yves Robert, Frédéric Vivien, and Dounia Zaidouni. Combining process replication and checkpointing for resilience on exascale systems. LAPACK Working Note 268, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, June 2012. URL http://

www.netlib.org/lapack/lawnspdf/lawn268.pdf. UT-CS-12-696.

Bosilca:2012:UMA

[268] George Bosilca, Aurelien Bouteiller, Elisabeth Brunet, Franck Cappello, Jack Dongarra, Amina Guermouche, Thomas Herault, Yves Robert, Frederic Vivien, and Dounia Zaidouni. Unified model for assessing checkpointing protocols at extreme-scale. LAPACK Working Note 269, Department of Computer Science, University of Tennessee, Knoxville, Knoxville,

TN 37996, USA, June 2012. URL http://www.netlib.org/lapack/
lawnspdf/lawn269.pdf. UT-CS-12-697.

Langou:2012:HLL

[269] Julie Langou, Bill Hofman, and Brad King. How LAPACK library enables Microsoft Visual Studio support with CMake and LAPACKE. LAPACK Working Note 270, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, July 2012. URL http://

www.netlib.org/lapack/lawnspdf/lawn270.pdf. UT-CS-12-698.

Karlsson:2012:OPC

[270] Lars Karlsson and Daniel Kressner. Optimally packed chains of bulges in multishift QR algorithms. LAPACK Working Note 271, Department of Computing Science, Umeå University and EPF, Umeå, Sweden and Lausanne, Switzerland, August 2012. URL http://www.netlib.org/

lapack/lawnspdf/lawn271.pdf.

Du:2012:PGC

[271] Peng Du, Stanimire Tomov, and Jack Dongarra. Providing GPU capability to LU and QR within the ScaLAPACK framework. LAPACK Working Note 272, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, September 2012. URL http://

www.netlib.org/lapack/lawnspdf/lawn272.pdf. UT-CS-12-699.

Baboulin:2012:ECC

[272] Marc Baboulin, Serge Gratton, Remi Lacroix, and Alan Laub. Efficient computation of condition estimates for linear least squares problems. LA-PACK Working Note 273, INRIA (Institut National de Recherche en Informatique et en Automatique), Rocquencourt, France, September 2012.

URL http://www.netlib.org/lapack/lawnspdf/lawn273.pdf. INRIA-

8065.

Dongarra:2012:RDC

[273] Jack Dongarra, Thomas Herault, and Yves Robert. Revisiting the double checkpointing algorithm. LAPACK Working Note 274, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN

37996, USA, December 2012. URL http://www.netlib.org/lapack/
lawnspdf/lawn274.pdf. UT-CS-13-705.

Cao:2013:CHP

[274] Chongxiao Cao, Jack Dongarra, Peng Du, Mark Gates, Piotr Luszczek, and Stanimire Tomov. clMAGMA: High performance dense linear algebra with OpenCL. LAPACK Working Note 275, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996,

USA, March 2013. URL http://www.netlib.org/lapack/lawnspdf/

lawn275.pdf. UT-CS-13-706.

Demmel:2013:CAR

[275] James W. Demmel, Laura Grigori, Ming Gu, and Hua Xiang. Communication avoiding rank revealing QR factorization with column pivoting. LAPACK Working Note 276, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, May 2013. URL

http://www.netlib.org/lapack/lawnspdf/lawn276.pdf. UCB/EECS-

2013-46.

Aupy:2013:ISA

[276] Guillaume Aupy, Mathieu Faverge, Yves Robert, Jakub Kurzak, Piotr Luszczek, and Jack Dongarra. Implementing a systolic algorithm for QR factorization on multicore clusters with PaRSEC. LAPACK Working Note 277, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, May 2013. URL http://www.netlib.org/

lapack/lawnspdf/lawn277.pdf. UT-CS-13-709.

Aupy:2013:CSE

[277] Guillaume Aupy, Anne Benoit, Thomas Hérault, Yves Robert, Frédéric Vivien, and Dounia Zaidouni. On the combination of silent error detection and checkpointing. LAPACK Working Note 278, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA,

June 2013. URL http://www.netlib.org/lapack/lawnspdf/lawn278.

pdf. UT-CS-13-710.

Jia:2013:TER

[278] Yulu Jia, Piotr Luszczek, and Jack Dongarra. Transient error resilient Hessenberg reduction on GPU-based hybrid architectures. LAPACK Working Note 279, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, June 2013. URL http://www.

netlib.org/lapack/lawnspdf/lawn279.pdf. UT-CS-13-712.

Donfack:2013:AVP

[279] Simplice Donfack, Jack Dongarra, Mathieu Faverge, Mark Gates, Jakub Kurzak, Piotr Luszczek, and Ichitaro Yamazaki. On algorithmic variants of parallel Gaussian elimination: Comparison of implementations in terms of performance and numerical properties. LAPACK Working Note 280, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, July 2013. URL http://www.netlib.org/

lapack/lawnspdf/lawn280.pdf. UT-CS-13-715.

Aupy:2013:OCP

[280] Guillaume Aupy, Anne Benoit, Thomas Herault, Yves Robert, and Jack Dongarra. Optimal checkpointing period: Time vs. energy. LAPACK Working Note 281, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, October 2013. URL http:

//www.netlib.org/lapack/lawnspdf/lawn281.pdf. UT-EECS-13-718.

Faverge:2013:DHS

[281] Mathieu Faverge, Julien Herrmann, Julien Langou, Bradley Lowery, Yves Robert, and Jack Dongarra. Designing LU–QR hybrid solvers for performance and stability. LAPACK Working Note 282, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996,

USA, October 2013. URL http://www.netlib.org/lapack/lawnspdf/

lawn282.pdf. UT-EECS-13-719.

Haidar:2013:IPS

[282] Azzam Haidar, Piotr Luszczek, Jakub Kurzak, and Jack Dongarra. An improved parallel singular value algorithm and its implementation for multicore hardware. LAPACK Working Note 283, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996,

USA, October 2013. URL http://www.netlib.org/lapack/lawnspdf/

lawn283.pdf. UT-EECS-13-720.

Kohler:2013:FFB

[283] Martin Köhler and Jens Saak. FlexiBLAS — a flexible BLAS library with runtime exchangeable backends. LAPACK Working Note 284, Department of Computer Science, University of Tennessee, Knoxville, Knoxville,

TN 37996, USA, ???? 2013. URL http://www.netlib.org/lapack/
lawnspdf/lawn284.pdf.

Baboulin:2014:URB

[284] Marc Baboulin, Xiaoye S. Li, and François-Henry Rouet. Using random butterfly transformations to avoid pivoting in sparse direct methods. LAPACK Working Note 285, Department of Computer Science, University of Tennessee, Knoxville, Knoxville, TN 37996, USA, Febru-

ary 2014. URL http://www.netlib.org/lapack/lawnspdf/lawn285.

pdf. Inria Research Report RR-8481.

Brewer:1988:TAAb

[285] Orlie Brewer, Jack Dongarra, and Danny Sorensen. Tools to aid in the analysis of memory access patterns for FORTRAN programs. Parallel Computing, 9(1):25–35, December 1988. CODEN PACOEJ. ISSN

0167-8191. URL http://www.netlib.org/utk/people/JackDongarra/
PAPERS/Tools-to-Aid-Analysis-of-Memory-Access-Patterns-for-FORTRAN-

Programs.pdf. See original LAPACK Working note in [6].

Bai:1989:BIHb

[286] Z. Bai and J. Demmel. On a block implementation of Hessenberg multishift QR iteration. International Journal of High Speed Computing (IJHSC), 1(1):97–112, 1989. CODEN IHSCEZ. ISSN 0129-0533. See original LAPACK Working note in [8].

Dongarra:1989:BRM

[287] J. J. Dongarra, D. C. Sorensen, and S. J. Hammarling. Block reduction of matrices to condensed forms for eigenvalue computations. Journal of Computational and Applied Mathematics, 27(1–2):215–227, September 1989. CODEN JCAMDI. ISSN 0377-0427 (print), 1879-1778 (electronic). See original LAPACK Working note in [2].

Anderson:1990:LPLb

[288] E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. DuCroz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen. LA-PACK: A portable linear algebra library for high-performance computers. In IEEE [371], pages 2–11. ISBN 0-8186-2056-0 (paperback) (IEEE Computer Society), 0-89791-412-0 (paperback) (ACM). LCCN QA 76.88 S87 1990. See original LAPACK Working note in [20].

Barlow:1990:CAE

[289] Jesse Barlow and James Demmel. Computing accurate eigensystems of scaled diagonally dominant matrices. SIAM Journal on Numerical Analysis, 27(3):762–791, June 1990. CODEN SJNAAM. ISSN 0036-1429 (print), 1095-7170 (electronic). See original LAPACK Working note in [7].

Dongarra:1990:ASL

[290] Jack J. Dongarra, Jeremy Du Croz, Sven Hammarling, and Iain Duff. Algorithm 679: A set of level 3 Basic Linear Algebra Subprograms: Model implementation and test programs. ACM Transactions on Mathematical Software, 16(1):18–28, March 1990. CODEN ACMSCU. ISSN 0098-3500 (print), 1557-7295 (electronic). URL http://www.acm.org/

pubs/citations/journals/toms/1990-16-1/p18-dongarra/. See also

[291, 300, 316].

Higham:1990:EFM

[291] Nicholas J. Higham. Exploiting fast matrix multiplication within the level 3 BLAS. ACM Transactions on Mathematical Software, 16(4): 352–368, December 1990. CODEN ACMSCU. ISSN 0098-3500 (print),

1557-7295 (electronic). URL http://www.acm.org/pubs/citations/
journals/toms/1990-16-4/p352-higham/. Describes algorithms based

on Strassen’s method which are asymptotically faster than the standard N^{3} algorithm, and in practice, faster for N ≈ 100, and examines their numerical stability. See [290, 300, 316].

Deift:1991:BSV

[292] Percy Deift, James Demmel, Luen Chau Li, and Carlos Tomei. The bidiagonal singular value decomposition and Hamiltonian mechanics. SIAM Journal on Numerical Analysis, 28(5):1463–1516, October 1991. CODEN SJNAAM. ISSN 0036-1429 (print), 1095-7170 (electronic). See original LAPACK Working note in [11].

Dongarra:1991:IRS

[293] J. J. Dongarra, P. Mayes, and G. Radicati di Brozolo. The IBM RISC System/6000 and linear algebra operations. Supercomputer, 8(4):15–30, July 1991. CODEN SPCOEL. ISSN 0168-7875. URL http://www.netlib.

org/utk/people/JackDongarra/PAPERS/The-IBM-RISC-System-6000-
and-Linear-Algebra-Operations.pdf. See original LAPACK Working

note in [28].

Anderson:1992:GFA

[294] E. Anderson, Z. Bai, and J. Dongarra. Generalized QR factorization and its applications. Linear Algebra and its Applications, 162/164:243–271, 1992. CODEN LAAPAW. ISSN 0024-3795 (print), 1873-1856 (elec-

tronic). URL http://www.netlib.org/utk/people/JackDongarra/
PAPERS/Generalized-QR-Factorization-and-Its-Applications.pdf.

Directions in matrix theory (Auburn, AL, 1990). See original LAPACK Working note in [31].

Bischof:1992:GIC

[295] Christian H. Bischof and Ping Tak Peter Tang. Generalizing incremental condition estimation. Journal of Numerical linear algebra with applications, 1(2):149–163, 1992. CODEN NLAAEM. ISSN 0129-3281. See original LAPACK Working note in [32].

Choi:1992:SSLb

[296] J. Choi, J. J. Dongarra, R. Pozo, and D. W. Walker. ScaLAPACK: a scalable linear algebra library for distributed memory concurrent computers. In Siegel [374], pages 120–127. ISBN 0-8186-2772-7 (hardback), 0-8186-2771-9 (microfiche). LCCN QA76.58 .S95 1992. IEEE catalog number 92CH3185-6. See original LAPACK Working note in [55].

Croz:1992:SMM

[297] Jeremy J. Du Croz and Nicholas J. Higham. Stability of methods for matrix inversion. IMA Journal of Numerical Analysis, 12:1–19, 1992. CODEN IJNADH. ISSN 0272-4979 (print), 1464-3642 (electronic). See original LAPACK Working note in [27].

Demmel:1992:DPH

[298] J. Demmel, J. Dongarra, and W. Kahan. On designing portable high performance numerical libraries. In Griffiths and Watson [372], page ?? ISBN 0-582-08908-5. LCCN QA297.D85 1991. See original LAPACK Working note in [39].

Demmel:1992:JMM

[299] James Demmel and Krešimir Veselić. Jacobi’s method is more accurate than QR. SIAM Journal on Matrix Analysis and Applications, 13(4): 1204–1245, October 1992. CODEN SJMAEL. ISSN 0895-4798 (print), 1095-7162 (electronic). See original LAPACK Working note in [15].

Demmel:1992:SBA

[300] James W. Demmel and Nicholas J. Higham. Stability of block algorithms with fast level-3 BLAS. ACM Transactions on Mathematical Software, 18(3):274–291, September 1992. CODEN ACMSCU. ISSN 0098-3500 (print), 1557-7295 (electronic). URL http://www.acm.org/pubs/toc/

Abstracts/0098-3500/131769.html. See [290, 291, 316]. See original

LAPACK Working note in [22].

Dongarra:1992:LASb

[301] J. Dongarra, R. van de Geijn, and D. Walker. A look at scalable dense linear algebra libraries. In IEEE [373], page ?? ISBN 0-8186-2775-1. LCCN QA76.76.A65 S33 1992. IEEE catalog number 92TH0432-5. See original LAPACK Working note in [44].

Dongarra:1992:NCC

[302] Jack J. Dongarra, Sven Hammarling, and James H. Wilkinson. Numerical considerations in computing invariant subspaces. SIAM Journal on Matrix Analysis and Applications, 13(1):145–161, January 1992. CODEN SJMAEL. ISSN 0895-4798 (print), 1095-7162 (electronic). See original LAPACK Working note in [25].

Dongarra:1992:RCFb

[303] Jack J. Dongarra and Robert A. van de Geijn. Reduction to condensed form for the eigenvalue problem on distributed memory architectures. Parallel Computing, 18(9):973–982, September 1992. CODEN

PACOEJ. ISSN 0167-8191. URL http://www.netlib.org/utk/people/
JackDongarra/PAPERS/Reduction-to-Condensed-Form-for-the-Eigenvalue-
Problem-on-Distributed-Memory.pdf. See original LAPACK Working

note in [30].

Anderson:1993:PLP

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Bai:1993:CGS

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Bai:1993:SDB

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Demmel:1993:CAS

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Demmel:1993:IEB

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Demmel:1993:PNLb

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Demmel:1993:TPN

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Dongarra:1993:TDB

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Higham:1993:PTB

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Choi:1994:DPD

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Choi:1994:PMT

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Choi:1994:PPU

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Dayde:1994:PBI

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Demmel:1994:FNA

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Dongarra:1994:SMLb

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vandeGeijn:1994:GCO

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Bai:1995:TLAb

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Choi:1995:DPDb

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Demmel:1995:CSB

[322] James W. Demmel, Inderjit Dhillon, and Huan Ren. On the correctness of some bisection-like parallel eigenvalue algorithms in floating point arithmetic. Electron. Trans. Numer. Anal., 3:116–149, 1995. See original LAPACK Working note in [70].

Heath:1995:CPN

[323] Michael T. Heath and Padma Raghavan. A Cartesian parallel nested dissection algorithm. SIAM Journal on Matrix Analysis and Applications, 16(1):235–253, January 1995. CODEN SJMAEL. ISSN 0895-4798 (print), 1095-7162 (electronic). URL http://epubs.siam.org/sam-bin/ dbq/article/23827. See original LAPACK Working note in [52].

Plank:1995:ADC

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Raghavan:1995:DSG

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Barrett:1996:ABI

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Blackford:1996:PEDb

[327] L. S. Blackford, A. Cleary, J. Demmel, I. Dhillon, J. Dongarra, S. Hammarling, A. Petitet, H. Ren, K. Stanley, and R. C. Whaley. Practical experience in the dangers of heterogeneous computing. In Waśniewski et al. [383], pages 57–64. ISBN 3-540-62095-8 (softcover). ISSN 0302-9743 (print), 1611-3349 (electronic). LCCN QA76.58 .P35 1996. URL

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Blackford:1996:SPL

[328] Laura Susan Blackford, J. Choi, A. Cleary, A. Petitet, R. C. Whaley, J. Demmel, I. Dhillon, K. Stanley, J. Dongarra, S. Hammarling, G. Henry, and D. Walker. ScaLAPACK: A portable linear algebra library for distributed memory computers — design issues and performance. In ACM [381], page ?? ISBN 0-89791-854-1. LCCN A76.88 .S8573 1996.

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Choi:1996:DIS

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Choi:1996:PSP

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Dongarra:1996:PFI

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Henry:1996:PAU

[332] Greg Henry and Robert van de Geijn. Parallelizing the QR algorithm for the unsymmetric algebraic eigenvalue problem: Myths and reality. SIAM Journal on Scientific Computing, 17(4):870–883, July 1996. CO-DEN SJOCE3. ISSN 1064-8275 (print), 1095-7197 (electronic). See original LAPACK Working note in [79].

Kaagstrom:1996:CES

[333] Bo Kågström and Peter Poromaa. Computing eigenspaces with specified eigenvalues of a regular matrix pair (A, B) and condition estimation: theory, algorithms and software. Numerical Algorithms, 12(3–4):369–407, July 1996. CODEN NUALEG. ISSN 1017-1398 (print), 1572-9265 (electronic). See original LAPACK Working note in [87].

Kaagstrom:1996:LSA

[334] Bo Kågström and Peter Poromaa. LAPACK-style algorithms and software for solving the generalized Sylvester equation and estimating the separation between regular matrix pairs. ACM Transactions on Mathematical Software, 22(1):78–103, March 1996. CODEN ACMSCU. ISSN 0098-3500 (print), 1557-7295 (electronic). URL http://www.acm.org/

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Lehoucq:1996:CEU

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Bai:1997:SDN

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Blackford:1997:PEN

[337] L. S. Blackford, A. Cleary, A. Petitet, R. C. Whaley, J. Demmel, I. Dhillon, H. Ren, K. Stanley, J. Dongarra, and S. Hammarling. Practical experience in the numerical dangers of heterogeneous computing. ACM Transactions on Mathematical Software, 23(2):133–147, June 1997. CODEN ACMSCU. ISSN 0098-3500 (print), 1557-7295 (electronic).

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Dongarra:1997:KCPb

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Higham:1997:IRL

[339] Nicholas J. Higham. Iterative refinement for linear systems and LA-PACK. IMA Journal of Numerical Analysis, 17(4):495–509, October 1997. CODEN IJNADH. ISSN 0272-4979 (print), 1464-3642 (elec-

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Higham:1997:SDP

[340] Nicholas J. Higham. Stability of the diagonal pivoting method with partial pivoting. SIAM Journal on Matrix Analysis and Applications, 18(1):52– 65, January 1997. CODEN SJMAEL. ISSN 0895-4798 (print), 1095-7162 (electronic). See original LAPACK Working note in [105].

Li:1997:RPB

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vandeGeijn:1997:SSU

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Choi:1998:NPM

[343] Jaeyoung Choi. A new parallel matrix multiplication algorithm on distributed-memory concurrent computers. Concurrency: Practice and Experience, 10(8):655–670, July 1998. CODEN CPEXEI. ISSN 1040-3108.

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Desprez:1998:SBA

[344] F. Desprez, J. Dongarra, A. Petitet, and C. Randriamaro. Scheduling block-cyclic array redistribution. In D’Hollander et al. [385], pages 227– 234. ISBN 0-444-82882-6. LCCN QA76.58.P3795 1997. See original LA-PACK Working note in [120] and [345].

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[345] F. Desprez, J. Dongarra, A. Petitet, C. Randriamaro, and Y. Robert. Scheduling block-cyclic array redistribution. IEEE Transactions on Parallel and Distributed Systems, 9(2):192–??, February 1998. CODEN ITDSEO. ISSN 1045-9219 (print), 1558-2183 (electronic). URL http:

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Dongarra:1998:HPL

[346] J. Dongarra and J. Waśniewski. High performance linear algebra package LAPACK90. Lecture Notes in Computer Science, 1388:387–391, 1998. CODEN LNCSD9. ISSN 0302-9743 (print), 1611-3349 (electronic). See original LAPACK Working note in [134].

Kaagstrom:1998:GBL

[347] Bo Kågström, Per Ling, and Charles Van Loan. GEMM-based level 3 BLAS: high-performance model implementations and performance evaluation benchmark. ACM Transactions on Mathematical Software, 24 (3):268–302, September 1998. CODEN ACMSCU. ISSN 0098-3500 (print), 1557-7295 (electronic). URL http://www.acm.org:80/pubs/

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Li:1998:RPT

[348] Ren-Cang Li. Relative perturbation theory: I. eigenvalue and singular value variations. SIAM Journal on Matrix Analysis and Applications, 19(4):956–982, October 1998. CODEN SJMAEL. ISSN 0895-4798 (print), 1095-7162 (electronic). URL http://epubs.siam.org/sam-bin/ dbq/article/29849. See original LAPACK Working note in [84].

Whaley:1998:ATL

[349] R. Clint Whaley and Jack J. Dongarra. Automatically Tuned Linear Algebra Software (ATLAS). In ACM [384], page ???? ISBN ????

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Arbenz:1999:CPSc

[350] P. Arbenz, A. Cleary, J. Dongarra, and M. Hegland. A comparison of parallel solvers for diagonally dominant and general narrow-banded linear systems. Parallel and Distributed Computing Practices, 2(4):??, ???? 1999.

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Demmel:1999:APS

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Demmel:1999:CSV

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Demmel:1999:SAS

[353] James W. Demmel, Stanley C. Eisenstat, John R. Gilbert, Xiaoye S. Li, and Joseph W. H. Liu. A supernodal approach to sparse partial pivoting. SIAM Journal on Matrix Analysis and Applications, 20(3):720–755, July 1999. CODEN SJMAEL. ISSN 0895-4798 (print), 1095-7162 (electronic).

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Li:1999:RPT

[354] Ren-Cang Li. Relative perturbation theory: II. eigenspace and singular subspace variations. SIAM Journal on Matrix Analysis and Applications, 20(2):471–492, April 1999. CODEN SJMAEL. ISSN 0895-4798 (print), 1095-7162 (electronic). URL http://epubs.siam.org/sam-bin/ dbq/article/29850. See original LAPACK Working note in [85].

Petitet:1999:ARM

[355] A. P. Petitet and J. J. Dongarra. Algorithmic redistribution methods for block-cyclic decompositions. IEEE Transactions on Parallel and Distributed Systems, 10(12):201–??, December 1999. CO-DEN ITDSEO. ISSN 1045-9219 (print), 1558-2183 (electronic).

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Petitet:1999:NLA

[356] A. Petitet, H. Casanova, R. Whaley, J. Dongarra, and Y. Robert. A numerical linear algebra problem solving environment designer’s perspective. In SIAM Annual Meeting, Atlanta, GA, May 13, 1999. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 1999.

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DAzevedo:2000:DIP

[357] Eduardo D’Azevedo and Jack Dongarra. The design and implementation of the parallel out-of-core ScaLAPACK LU, QR, and Cholesky factorization routines. Concurrency: Practice and Experience, 12(15):1481– 1493, ???? 2000. CODEN CPEXEI. ISSN 1040-3108. URL http://

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Parlett:2000:IAP

[358] Beresford N. Parlett and Osni A. Marques. An implementation of the dqds algorithm (positive case). Linear Algebra and its Applications, 309(1–3): 217–259, April 15, 2000. CODEN LAAPAW. ISSN 0024-3795 (print),

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Petitet:2000:PDS

[359] A. Petitet, H. Casanova, J. Dongarra, Y. Robert, and R. Whaley. Parallel and distributed scientific computing: A numerical linear algebra problem solving environment designer’s perspective. In Jacek Blazewicz et al., editors, Handbook on Parallel and Distributed Processing, page ?? Springer-Verlag, Berlin, Germany / Heidelberg, Germany / London, UK / etc., 2000. ISBN 3-540-66441-6. LCCN QA76.58 .H36 2000. URL http://www.

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Andersen:2001:RFC

[360] Bjarne S. Andersen, Jerzy Waśniewski, and Fred G. Gustavson. A recursive formulation of Cholesky factorization of a matrix in packed storage. ACM Transactions on Mathematical Software, 27(2):214–244, June 2001. CODEN ACMSCU. ISSN 0098-3500 (print), 1557-7295 (electronic). See original LAPACK Working note in [146].

Whaley:2001:AEO

[361] R. Clint Whaley, Antoine Petitet, and Jack J. Dongarra. Automated empirical optimizations of software and the ATLAS project. Parallel Computing, 27(1–2):3–35, January 2001. CODEN PACOEJ. ISSN 0167-

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Bindel:2002:CGR

[362] David Bindel, James Demmel, William Kahan, and Osni Marques. On computing Givens rotations reliably and efficiently. ACM Transactions on Mathematical Software, 28(2):206–238, June 2002. CODEN ACMSCU. ISSN 0098-3500 (print), 1557-7295 (electronic). URL all

previous codes occasionally suffer   from large inaccuracies
due to over/underflow. For real Givens rotations   there are
also improvements in speed and accuracy, though not as striking.
 Third, the design process that led to this reliable implementation
is quite   systematic, and could be applied to the design of
similarly reliable   subroutines.. See original LAPACK Working

note in [148].

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