A de Montessus type convergence study of a least-squares vector-valued rational interpolation procedure

Authors:
Avram Sidi
Affiliations:
Computer Science Department, Technion - Israel Institute of Technology, Haifa 32000, Israel
Venue:
Journal of Approximation Theory
Year:
2008

Citing 8
Cited 1

Acceleration of convergence of vector sequences

SIAM Journal on Numerical Analysis
Row convergence theorems for generalised inverse vector-valued Pade´ approximants

Journal of Computational and Applied Mathematics
Quantitative and constructive aspects of the generalized Koenig's and de Montessus's theorems for Pade´ approximants

Journal of Computational and Applied Mathematics
An extension of a row convergence theorem for vector Pade´ approximants

Journal of Computational and Applied Mathematics
Rational approximations from power series of vector-valued meromorphic functions

Journal of Approximation Theory
The Richardson Extrapolation Process with a Harmonic Sequence of Collocation Points

SIAM Journal on Numerical Analysis
A new approach to vector-valued rational interpolation

Journal of Approximation Theory
Algebraic properties of some new vector-valued rational interpolants

Journal of Approximation Theory

Full length article: Incomplete Padé approximation and convergence of row sequences of Hermite-Padé approximants

Journal of Approximation Theory

Quantified Score

Hi-index	0.00

Visualization

Abstract

In a recent paper of the author [A. Sidi, A new approach to vector-valued rational interpolation, J. Approx. Theory 130 (2004) 177-187], three new interpolation procedures for vector-valued functions F(z), where F:C-C^N, were proposed, and some of their algebraic properties were studied. One of these procedures, denoted IMPE, was defined via the solution of a linear least-squares problem. In the present work, we concentrate on IMPE, and study its convergence properties when it is applied to meromorphic functions with simple poles and orthogonal vector residues. We prove de Montessus and Koenig type theorems when the points of interpolation are chosen appropriately.