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Rational Approximations of PSWFs

  • Andrei Osipov
  • Vladimir Rokhlin
  • Hong Xiao
Chapter
Part of the Applied Mathematical Sciences book series (AMS, volume 187)

Abstract

In this chapter, we construct rational approximations of PSWFs. More specifically, we approximate the reciprocal of ψ n in the interval ( −1,1) by a rational function having n poles (these poles happen to be precisely the n roots of ψ n in (−1,1)). Also, we derive explicit bounds on the error of such approximations. The underlying analysis is based on a detailed investigation of certain properties of PSWFs outside the interval (−1,1) (see also [49, 50]).

Keywords

Rational Approximation Prolate Index Boundary Term Fourth Column Principal Result 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Bibliography

  1. [49]
    A. Osipov, V. Rokhlin, Detailed analysis of prolate quadratures and interpolation formulas, Yale CS Technical Report #1458, 2012.Google Scholar
  2. [50]
    A. Osipov, V. Rokhlin, Detailed analysis of prolate quadratures and interpolation formulas, arXiv:1208.4816v1, 2012.Google Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Andrei Osipov
    • 1
  • Vladimir Rokhlin
    • 2
  • Hong Xiao
    • 3
  1. 1.Department of MathematicsYale UniversityNew HavenUSA
  2. 2.Department of Computer ScienceYale UniversityNew HavenUSA
  3. 3.Department of Computer ScienceUniversity of CaliforniaDavisUSA

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