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BibTeX entry
@Article{Parlett:2000:TR,
author = "Beresford N. Parlett",
title = "For tridiagonals {$T$} replace {$T$} with {$ L D L^t
$}",
journal = j-J-COMPUT-APPL-MATH,
volume = "123",
number = "1--2",
pages = "117--130",
day = "1",
month = nov,
year = "2000",
CODEN = "JCAMDI",
DOI = "https://doi.org/10.1016/S0377-0427(00)00394-0",
ISSN = "0377-0427 (print), 1879-1778 (electronic)",
ISSN-L = "0377-0427",
MRclass = "65F10 (65F35)",
MRnumber = "MR1798522 (2001j:65055)",
bibdate = "Sat Feb 25 12:43:37 MST 2017",
bibsource = "http://www.math.utah.edu/pub/bibnet/authors/p/parlett-beresford-n.bib;
http://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
note = "Numerical analysis 2000, Vol. III. Linear algebra",
URL = "http://www.sciencedirect.com/science/article/pii/S0377042700003940",
ZMnumber = "0970.65032",
abstract = "The author discusses two of the ideas needed to
compute eigenvectors that are orthogonal without making
use of the Gram--Schmidt procedure when some of the
eigenvalues are tightly clustered. In the first of the
new schemes, the radical new goal is to compute an
approximate eigenvector for a given approximate
eigenvalue with a relative residual property. In the
second scheme, due to the relative gaps in the spectrum
the origin is shifted and the triangular factorization
is used. In the development, the recently discovered
differential stationary QD algorithms are used.
Examples of both ideas, using four by four systems, are
given",
acknowledgement = ack-nhfb,
classmath = "*65F15 Eigenvalues (numerical linear algebra) 65F05
Direct methods for linear systems",
fjournal = "Journal of Computational and Applied Mathematics",
journal-URL = "http://www.sciencedirect.com/science/journal/03770427",
keywords = "clustered eigenvalues; eigenvalue; LDU factorization;
numerical examples; orthogonal eigenvectores; QD
algorithm; triangular factorization",
reviewer = "R. P. Tewarson (Stony Brook)",
}
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113(1)153,
114(2)367,
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115(1)63,
115(1)397,
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123(1)261,
124(1)ix--x,
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125(1)57,
125(1)131,
125(1)265,
125(1)297,
125(1)395,
127(1)287,
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128(1)1,
132(1)141,
132(2)255,
133(1)127,
133(1)535,
133(1)601,
133(1)623,
134(1)143,
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137(2)377,
139(2)239,
139(2)323,
140(1)751,
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168(1)65,
168(1)77,
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168(1)289,
168(1)353,
169(2)377,
171(1)199
- approximate,
113(1)17,
123(1)293,
128(1)447,
134(1)85,
140(1)13,
157(2)309
- author,
113(1)411,
121(1)379,
127(1)369,
128(1)467,
129(1)209,
130(1)387,
130(1)389,
131(1)507,
132(2)483,
133(1)703,
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135(2)335,
136(1)405,
137(2)399,
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141(1)283,
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170(2)469,
171(1)425,
172(2)409
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117(1)35
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121(1)125,
124(1)1,
124(1)209,
128(1)133,
133(1)183,
156(2)433,
164(z)673,
168(1)341
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130(1)173,
167(2)485
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113(1)227,
115(1)151,
117(1)17,
117(2)91,
123(1)35,
123(1)67,
123(1)101,
123(1)155,
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161(2)339,
163(1)79,
163(1)101,
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171(1)291,
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171(1)367
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126(1)369,
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162(2)299,
166(2)565
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130(1)197,
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140(1)479,
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140(1)231,
162(1)287,
164(z)661
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148(1)169
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113(1)73,
121(1)379,
140(1)837,
164(z)783
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115(1)101,
115(1)331,
118(1)43,
119(1)29,
119(1)115,
119(1)185,
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123(1)515,
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137(1)145,
138(2)287,
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150(2)219,
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156(1)77,
156(1)179,
157(1)57,
158(2)419,
159(1)65,
159(2)365,
160(1)265,
161(1)1,
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162(1)1,
162(1)147,
163(2)381,
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167(2)465,
169(1)235,
170(1)103,
170(2)255,
170(2)269,
170(2)371,
171(1)103,
172(1)169
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115(1)461,
116(2)201,
117(2)175,
119(1)81,
126(1)269,
126(1)287,
130(1)293,
130(1)369,
131(1)35,
131(1)65,
131(1)89,
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133(1)183,
133(1)383,
133(1)489,
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133(1)688,
136(1)99,
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148(2)349,
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153(1)543,
154(2)247,
155(2)307,
156(2)253,
158(2)277,
159(2)325,
162(2)299,
164(z)175,
164(z)749,
170(2)241,
171(1)411,
172(1)41
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115(1)503,
151(2)355,
164(z)323,
168(1)107,
168(1)365
- property,
114(1)23,
114(2)305,
117(2)175,
122(1)329,
131(1)497,
131(1)505,
133(1)231,
133(1)253,
133(1)387,
134(1)37,
137(2)269,
146(2)277,
146(2)361,
148(1)239,
148(1)267,
150(2)293,
152(1)289,
153(1)109,
155(2)383,
160(1)9,
160(1)259,
161(2)371,
163(1)253,
164(z)93,
164(z)107,
164(z)131,
164(z)723,
167(2)489,
169(2)297,
172(2)375
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123(1)131,
171(1)123
- residual,
123(1)261,
132(2)371,
150(2)357
- scheme,
115(1)181,
129(1)89,
131(1)1,
132(2)431,
133(1)151,
133(1)579,
133(1)623,
134(1)343,
137(1)1,
137(2)229,
140(1)809,
143(1)49,
145(1)247,
147(1)121,
151(2)335,
154(2)341,
154(2)415,
154(2)447,
155(1)163,
155(2)339,
161(1)119,
161(2)469,
163(1)189,
168(1)447,
168(1)481,
169(1)17
- schemes,
119(1)133,
119(1)275,
132(1)107,
132(2)277,
134(1)37,
134(1)59,
138(1)93,
138(1)173,
138(2)297,
140(1)849,
143(1)9,
144(1)263,
145(1)31,
145(1)183,
145(1)213,
152(1)305,
156(1)47,
158(1)19,
164(z)53,
164(z)195,
166(1)31,
167(1)227
- second,
113(1)51,
115(1)193,
130(1)369,
136(1)149,
141(1)187,
143(1)49,
143(2)275,
145(1)167,
145(2)493,
147(1)41,
154(2)431,
157(1)93,
170(2)455
- spectrum,
125(1)385,
148(1)77,
148(1)287,
161(2)313,
171(1)247
- stationary,
136(1)317,
154(2)447,
164(z)691,
168(1)299
- triangular,
119(1)259,
140(1)673,
156(1)47,
158(2)233,
167(1)227,
168(1)179
- tridiagonal,
133(1)413,
153(1)89,
156(1)179,
169(1)87
- two,
113(1)27,
114(1)189,
118(1)43,
118(1)71,
125(1)83,
130(1)205,
134(1)259,
137(1)77,
137(1)109,
142(1)115,
144(1)349,
152(1)467,
153(1)61,
157(2)297,
158(1)1,
161(2)371,
164(z)731,
169(2)345
- use,
116(1)93,
121(1)379,
133(1)111,
150(2)375,
152(1)199,
167(2)293,
167(2)321
- used,
147(2)333,
164(z)587
- using,
114(1)189,
114(2)247,
115(1)519,
115(1)593,
116(1)121,
119(1)249,
120(1)27,
121(1)113,
122(1)231,
125(1)183,
126(1)77,
129(1)89,
130(1)323,
130(1)369,
131(1)381,
132(2)387,
133(1)535,
133(1)545,
136(1)135,
140(1)209,
140(1)479,
140(1)499,
140(1)537,
140(1)727,
144(1)233,
146(1)155,
147(2)385,
149(1)359,
152(1)83,
152(1)377,
152(1)587,
153(1)395,
154(1)63,
154(1)175,
157(1)107,
158(1)11,
159(1)25,
159(1)85,
159(1)119,
159(2)365,
163(1)1,
166(2)565,
167(2)417,
168(1)11,
168(1)225,
168(1)481,
170(1)27,
170(2)461,
172(1)169,
172(2)337,
176(2)259
- Vol,
121(1)ix--x,
122(1)ix--xi,
123(1)ix--xii,
123(1)35,
124(1)ix--x,
125(1)xi--xviii,
128(1)ix--xi