Algebraic properties of robust Padé approximants

Beckermann, Bernhard; Matos, Ana

Document type :

Article dans une revue scientifique: Article original

Permalink :

http://hdl.handle.net/20.500.12210/120653

Title :

Algebraic properties of robust Padé approximants

Author(s) :

Beckermann, Bernhard [Auteur]

Laboratoire Paul Painlevé - UMR 8524 [LPP]
Matos, Ana [Auteur correspondant]

Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Journal of Approximation Theory

Pages :

91-115

Publisher :

Elsevier

Publication date :

2015

ISSN :

0021-9045

Keyword(s) :

Padé approximation
SVD
regularization
Froissart doublet
spurious poles

HAL domain(s) :

Mathématiques [math]/Analyse numérique [math.NA]

English abstract : [en]

For a recent new numerical method for computing so-called robust Padé approximants through SVD techniques, the authors gave numerical evidence that such approximants are insensitive to perturbations in the data, and do not ...
Show more >For a recent new numerical method for computing so-called robust Padé approximants through SVD techniques, the authors gave numerical evidence that such approximants are insensitive to perturbations in the data, and do not have so-called spurious poles, that is, poles with a close-by zero or poles with small residuals. A black box procedure for eliminating spurious poles would have a major impact on the convergence theory of Padé approximants since it is known that convergence in capacity plus absence of poles in some domain D implies locally uniform convergence in D. In the present paper we provide a proof for forward stability (or robustness), and show absence of spurious poles for the subclass of so-called well-conditioned Padé approximants. We also give a numerical example of some robust Padé approximant which has spurious poles, and discuss related questions. It turns out that it is not sufficient to discuss only linear algebra properties of the underlying rectangular Toeplitz matrix, since in our results other matrices like Sylvester matrices also occur. These types of matrices have been used before in numerical greatest common divisor computations.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Non spécifiée

Popular science :

Non

Comment :

20 pages

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Submission date :

2025-01-24T10:08:25Z

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