A new approach to vector-valued rational interpolation

Authors:
Avram Sidi
Affiliations:
Computer Science Department, Technion-Israel Institute of Technology, Technion City, Haifa 32000, Israel
Venue:
Journal of Approximation Theory
Year:
2004

Citing 3
Cited 2

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Application of Vector-Valued Rational Approximations to the Matrix Eigenvalue Problemand Connections with Krylov Subspace Methods

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Algebraic properties of some new vector-valued rational interpolants

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

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Abstract

In this work we propose three different procedures for vector-valued rational interpolation of a function F(z), where F : ¢ → ¢N, and develop algorithms for constructing the resulting rational functions. We show that these procedures also cover the general case in which some or all points of interpolation coalesce. In particular, we show that, when all the points of interpolation collapse to the same point, the procedures reduce to those presented and analyzed in an earlier paper [J. Approx. Theory 77 (1994) 89] by the author, for vector-valued rational approximations from Maclaurin series of F(z). Determinant representations for the relevant interpolants are also derived.