Rational Hermite-Padé Approximants vs Padé Approximants. Numerical Results

The main purpose of the paper is to present some powerful data on the advantage of the rational approximation procedure based on Hermite-Padé polynomials over the Padé approximation procedure. The first part of the paper is devoted to some numerical examples in this direction. The second part will b...

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Bibliographic Details
Published in:arXiv.org 2023-12
Main Authors: Dobrolyubov, Egor O, Ikonomov, Nikolay R, Knizhnerman, Leonid A, Suetin, Sergey P
Format: Article
Language:English
Subjects:
Hermite polynomials
Mathematical analysis
Pade approximation
Online Access:Get full text
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Summary:The main purpose of the paper is to present some powerful data on the advantage of the rational approximation procedure based on Hermite-Padé polynomials over the Padé approximation procedure. The first part of the paper is devoted to some numerical examples in this direction. The second part will be devoted to some theoretical results. In particular, we demonstrate our ideas about the advantage of rational Hermite-Padé approximants over Padé approximants analyzing the analytical structure of the frequency function \(\nu\) of the free Van der Pol equation.
ISSN:2331-8422