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Laurent Series and their Padé Approximations

  • Adhemar Bultheel

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

Table of contents

  1. Front Matter
    Pages i-xi
  2. Adhemar Bultheel
    Pages 1-10
  3. Adhemar Bultheel
    Pages 29-30
  4. Adhemar Bultheel
    Pages 37-46
  5. Adhemar Bultheel
    Pages 47-53
  6. Adhemar Bultheel
    Pages 55-63
  7. Adhemar Bultheel
    Pages 65-82
  8. Adhemar Bultheel
    Pages 131-139
  9. Adhemar Bultheel
    Pages 141-154
  10. Adhemar Bultheel
    Pages 155-165
  11. Adhemar Bultheel
    Pages 173-185
  12. Adhemar Bultheel
    Pages 187-194
  13. Adhemar Bultheel
    Pages 195-205
  14. Adhemar Bultheel
    Pages 207-232
  15. Adhemar Bultheel
    Pages 233-256
  16. Back Matter
    Pages 257-274

About this book

Introduction

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.

Keywords

Finite Matrix Meromorphic function algorithms behavior boundary element method convergence eXist filtering form graphs numerical analysis stochastic process symmetry systems theory

Authors and affiliations

  • Adhemar Bultheel
    • 1
  1. 1.Dept. Computer ScienceK. U. LeuvenLeuven-HeverleeBelgium

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