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Laurent Series and their Padé Approximations

  • Book
  • © 1987

Overview

Authors:
  1. Adhemar Bultheel

    1. Dept. Computer Science, K. U. Leuven, Leuven-Heverlee, Belgium

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Part of the book series: Operator Theory: Advances and Applications (OT, volume 27)

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Introduction

    • Adhemar Bultheel
    Pages 1-10

  3. Moebius transforms, continued fractions and Padé approximants

    • Adhemar Bultheel
    Pages 11-28

  4. Two algorithms

    • Adhemar Bultheel
    Pages 29-30

  5. All kinds of Padé Approximants

    • Adhemar Bultheel
    Pages 37-46

  6. Continued fractions

    • Adhemar Bultheel
    Pages 47-53

  7. Moebius transforms

    • Adhemar Bultheel
    Pages 55-63

  8. Rhombus algorithms

    • Adhemar Bultheel
    Pages 65-82

  9. Biorthogonal polynomials, quadrature and reproducing kernels

    • Adhemar Bultheel
    Pages 83-102

  10. Determinant expressions and matrix interpretations

    • Adhemar Bultheel
    Pages 103-129

  11. Symmetry Properties

    • Adhemar Bultheel
    Pages 131-139

  12. Block structures

    • Adhemar Bultheel
    Pages 141-154

  13. Meromorphic functions and asymptotic behaviour

    • Adhemar Bultheel
    Pages 155-165

  14. Montessus de Ballore theorem for Laurent-Padé approximants

    • Adhemar Bultheel
    Pages 167-171

  15. Determination of poles

    • Adhemar Bultheel
    Pages 173-185

  16. Determination of zeros

    • Adhemar Bultheel
    Pages 187-194

  17. Convergence in a row of the Laurent-Padé table

    • Adhemar Bultheel
    Pages 195-205

  18. The positive definite case and applications

    • Adhemar Bultheel
    Pages 207-232

  19. Examples

    • Adhemar Bultheel
    Pages 233-256

  20. Back Matter

    Pages 257-274
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Keywords

About this book

The Pade approximation problem is, roughly speaking, the local approximation of analytic or meromorphic functions by rational ones. It is known to be important to solve a large scale of problems in numerical analysis, linear system theory, stochastics and other fields. There exists a vast literature on the classical Pade problem. However, these papers mostly treat the problem for functions analytic at 0 or, in a purely algebraic sense, they treat the approximation of formal power series. For certain problems however, the Pade approximation problem for formal Laurent series, rather than for formal power series seems to be a more natural basis. In this monograph, the problem of Laurent-Pade approximation is central. In this problem a ratio of two Laurent polynomials in sought which approximates the two directions of the Laurent series simultaneously. As a side result the two-point Pade approximation problem can be solved. In that case, two series are approximated, one is a power series in z and the other is a power series in z-l. So we can approximate two, not necessarily different functions one at zero and the other at infinity.

Authors and Affiliations

  • Dept. Computer Science, K. U. Leuven, Leuven-Heverlee, Belgium

    Adhemar Bultheel

Bibliographic Information

  • Book Title: Laurent Series and their Padé Approximations

  • Authors: Adhemar Bultheel

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-9306-0

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 1987

  • Hardcover ISBN: 978-3-7643-1940-3Due: 01 January 1987

  • Softcover ISBN: 978-3-0348-9988-8Published: 03 October 2013

  • eBook ISBN: 978-3-0348-9306-0Published: 06 December 2012

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: XI, 276

  • Topics: Science, Humanities and Social Sciences, multidisciplinary

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