View in EDS

FAST AND STABLE RATIONAL INTERPOLATION IN ROOTS OF UNITY AND CHEBYSHEV POINTS.

Saved in:
Bibliographic Details
Title: FAST AND STABLE RATIONAL INTERPOLATION IN ROOTS OF UNITY AND CHEBYSHEV POINTS.
Authors: Pachón, Ricardo1 pachon@maths.ox.ac.uk, Gonnet, Pedro1 gonnet@maths.ox.ac.uk, Van Deun, Joris2 joris.vandeun@ua.ac.be
Source: SIAM Journal on Numerical Analysis. 2012, Vol. 50 Issue 3, p1713-1734. 22p.
Subjects: Interpolation, Numerical analysis, Chebyshev approximation, Fourier transforms, Linear differential equations
Abstract: A new method for interpolation by rational functions of prescribed numerator and denominator degrees is presented. When the interpolation nodes are roots of unity or Chebyshev points, the algorithm is particularly simple and relies on discrete Fourier transform matrices, which results in a fast implementation using the fast Fourier transform. The method is generalized for arbitrary grids, which requires the construction of polynomials orthogonal on the set of interpolation nodes. The appearance of common factors in the numerator and denominator due to finite-precision arithmetic is explained by the behavior of the singular values of the linear system associated with the rational interpolation problem. The new algorithm has connections with other methods, particularly the work of Jacobi and Kronecker, Berrut and Mittelmann, and Eğgecioğlu and Koç. Short MATLAB codes and numerical experiments are included. [ABSTRACT FROM AUTHOR]
Copyright of SIAM Journal on Numerical Analysis is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
FullText Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 82155395
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: FAST AND STABLE RATIONAL INTERPOLATION IN ROOTS OF UNITY AND CHEBYSHEV POINTS.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Pachón%2C+Ricardo%22">Pachón, Ricardo</searchLink><relatesTo>1</relatesTo><i> pachon@maths.ox.ac.uk</i><br /><searchLink fieldCode="AR" term="%22Gonnet%2C+Pedro%22">Gonnet, Pedro</searchLink><relatesTo>1</relatesTo><i> gonnet@maths.ox.ac.uk</i><br /><searchLink fieldCode="AR" term="%22Van+Deun%2C+Joris%22">Van Deun, Joris</searchLink><relatesTo>2</relatesTo><i> joris.vandeun@ua.ac.be</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22SIAM+Journal+on+Numerical+Analysis%22">SIAM Journal on Numerical Analysis</searchLink>. 2012, Vol. 50 Issue 3, p1713-1734. 22p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Interpolation%22">Interpolation</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Chebyshev+approximation%22">Chebyshev approximation</searchLink><br /><searchLink fieldCode="DE" term="%22Fourier+transforms%22">Fourier transforms</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+differential+equations%22">Linear differential equations</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: A new method for interpolation by rational functions of prescribed numerator and denominator degrees is presented. When the interpolation nodes are roots of unity or Chebyshev points, the algorithm is particularly simple and relies on discrete Fourier transform matrices, which results in a fast implementation using the fast Fourier transform. The method is generalized for arbitrary grids, which requires the construction of polynomials orthogonal on the set of interpolation nodes. The appearance of common factors in the numerator and denominator due to finite-precision arithmetic is explained by the behavior of the singular values of the linear system associated with the rational interpolation problem. The new algorithm has connections with other methods, particularly the work of Jacobi and Kronecker, Berrut and Mittelmann, and Eğgecioğlu and Koç. Short MATLAB codes and numerical experiments are included. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of SIAM Journal on Numerical Analysis is the property of Society for Industrial & Applied Mathematics and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=82155395
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1137/100797291
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 22
        StartPage: 1713
    Subjects:
      – SubjectFull: Interpolation
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Chebyshev approximation
        Type: general
      – SubjectFull: Fourier transforms
        Type: general
      – SubjectFull: Linear differential equations
        Type: general
    Titles:
      – TitleFull: FAST AND STABLE RATIONAL INTERPOLATION IN ROOTS OF UNITY AND CHEBYSHEV POINTS.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Pachón, Ricardo
      – PersonEntity:
          Name:
            NameFull: Gonnet, Pedro
      – PersonEntity:
          Name:
            NameFull: Van Deun, Joris
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 05
              Text: 2012
              Type: published
              Y: 2012
          Identifiers:
            – Type: issn-print
              Value: 00361429
          Numbering:
            – Type: volume
              Value: 50
            – Type: issue
              Value: 3
          Titles:
            – TitleFull: SIAM Journal on Numerical Analysis
              Type: main
ResultId 1