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On the conditioning of the Padé approximation problem

  • Luc Wuytack
Part I: Invited Speakers
Part of the Lecture Notes in Mathematics book series (LNM, volume 888)

Abstract

Several aspects of the conditioning of the Padé approximation problem are considered. The first is concerned with the operator that associates a power series f with its Padé approximant of a certain order. It is shown that this operator satisfies a local Lipschitz condition, in case the Padé approximant is normal.

The second aspect is the conditioning of the Padé approximant itself. It is indicated how this rational function r should be represented such that changes in its coefficients will effect changes on r as less as possible. A “condition number” for this problem is introduced.

The third aspect is the problem of the representation of the Padé approximant, such that the determination of its coefficients be a well-conditioned problem. It is known that the choice of powers of x as base functions can result in an ill-conditioned problem for the determination of the coefficients. The possibility of using other base functions is analysed.

Keywords

Base Function Rational Function Condition Number Toeplitz Matrix Hankel Matrix 
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.

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Copyright information

© Srpinger-Verlag 1981

Authors and Affiliations

  • Luc Wuytack
    • 1
  1. 1.Department of MathematicsUniversity of AntwerpWilrijkBelgium

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