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A de Montessus Type Convergence Study of a Least-Squares Vector-Valued Rational Interpolation Procedure II

A de Montessus Type Convergence Study of a Least-Squares Vector-Valued Rational Interpolation... We continue our study of convergence of IMPE, one of the vector-valued rational interpolation procedures proposed by the author in a recent paper, in the context of vector-valued meromorphic functions with simple poles. So far, this study has been carried out in the presence of corresponding residues that are mutually orthogonal. In the present work, we continue to study IMPE in the same context, but in the presence of corresponding residues that are not necessarily orthogonal. Choosing the interpolation points appropriately, we derive de Montessus type convergence results for the interpolants and König type results for the poles and residues. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

A de Montessus Type Convergence Study of a Least-Squares Vector-Valued Rational Interpolation Procedure II

Computational Methods and Function Theory , Volume 10 (1) – Feb 6, 2010

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References (27)

Publisher
Springer Journals
Copyright
Copyright © 2010 by Heldermann  Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321765
Publisher site
See Article on Publisher Site

Abstract

We continue our study of convergence of IMPE, one of the vector-valued rational interpolation procedures proposed by the author in a recent paper, in the context of vector-valued meromorphic functions with simple poles. So far, this study has been carried out in the presence of corresponding residues that are mutually orthogonal. In the present work, we continue to study IMPE in the same context, but in the presence of corresponding residues that are not necessarily orthogonal. Choosing the interpolation points appropriately, we derive de Montessus type convergence results for the interpolants and König type results for the poles and residues.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Feb 6, 2010

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