Entry Stenger:2000:SSN from jcomputapplmath2000.bib

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BibTeX entry

@Article{Stenger:2000:SSN,
  author =       "Frank Stenger",
  title =        "Summary of {Sinc} numerical methods",
  journal =      j-J-COMPUT-APPL-MATH,
  volume =       "121",
  number =       "1--2",
  pages =        "379--420",
  day =          "1",
  month =        sep,
  year =         "2000",
  CODEN =        "JCAMDI",
  DOI =          "https://doi.org/10.1016/s0377-0427(00)00348-4;
                 https://doi.org/10.1137/0712022",
  ISSN =         "0377-0427 (print), 1879-1778 (electronic)",
  ISSN-L =       "0377-0427",
  MRclass =      "65D15 (65-02)",
  MRnumber =     "MR1780056 (2001d:65018)",
  bibdate =      "Sat Feb 25 12:43:36 MST 2017",
  bibsource =    "http://www.math.utah.edu/pub/bibnet/authors/s/stenger-frank.bib;
                 http://www.math.utah.edu/pub/tex/bib/jcomputapplmath2000.bib",
  note =         "Numerical analysis in the 20th century, Vol.\ I,
                 Approximation theory",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0377042700003484",
  ZMnumber =     "0964.65010",
  abstract =     "This article attempts to summarize the existing
                 numerical methods based on Sinc approximation. Starting
                 with a comparison of polynomial and Sinc approximation,
                 basic formulas for the latter in the one-dimensional
                 case are given. The author also covers the
                 following:\par (i) Explicit spaces of analytic
                 functions for one dimensional Sinc approximation,\par
                 (ii) applications of Sinc indefinite integration and
                 collocation to the solution of ordinary differential
                 equation initial and boundary value problems,\par (iii)
                 results obtained for solution of partial differential
                 equations, via Sinc approximation of the
                 derivatives,\par (iv) some results obtained on the
                 solutions of integral equations,\par (v) use of Sinc
                 convolution, a technique for evaluating one and
                 multi-dimensional convolution-type integrals.\par A
                 list of some existing computer algorithms based on Sinc
                 methods is also given.",
  abstract2 =    "Sinc approximation methods excel for problems whose
                 solutions may have singularities, or infinite domains,
                 or boundary layers. This article summarizes results
                 obtained to date, on Sinc numerical methods of
                 computation. Sinc methods provide procedures for
                 function approximation over bounded or unbounded
                 regions, encompassing interpolation, approximation of
                 derivatives, approximate definite and indefinite
                 integration, solving initial value ordinary
                 differential equation problems, approximation and
                 inversion of Fourier and Laplace transforms,
                 approximation of Hilbert transforms, and approximation
                 of indefinite convolutions, the approximate solution of
                 partial differential equations, and the approximate
                 solution of integral equations, methods for
                 constructing conformal maps, and methods for analytic
                 continuation. Indeed, Sinc are ubiquitous for
                 approximating every operation of calculus.",
  acknowledgement = ack-nhfb,
  classmath =    "65D15 (Algorithms for functional approximation) 65-02
                 (Research monographs (numerical analysis)) 65L60
                 (Finite numerical methods for ODE) 65M70 (Spectral,
                 collocation and related methods (IVP of PDE)) 65N35
                 (Collocation methods (BVP of PDE)) 65R20 (Integral
                 equations (numerical methods)) 65T40 (Trigonometric
                 approximation and interpolation)",
  fjournal =     "Journal of Computational and Applied Mathematics",
  journal-URL =  "http://www.sciencedirect.com/science/journal/03770427",
  keywords =     "algorithms; analytic functions; collocation;
                 convolution-type integrals; integral equations; Sinc
                 indefinite integration; Sinc methods; survey article",
  reviewer =     "H. P. Dikshit (Bhopal)",
}

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