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A general module theoretic framework for vector M-Padé and matrix rational interpolation

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Abstract

A general module theoretic framework is used to solve several classical interpolation problems and generalizations thereof in a unified way. These problems are divided into two main families. The first family contains the classical linearized Padé, Padé-Hermite and M-Padé problems and the generalization to the vector M-Padé problem. The second family consists of the Padé problem, the scalar, vector and matrix rational interpolation problems. The solution method is straightforward, recursive and efficient. It can follow any “path” in the “solution table” even if this “solution table” is nonnormal (nonperfect). Reordering of the interpolation data is not required.

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Authors and Affiliations

  1. Department of Computer Science, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001, Leuven (Heverlee), Belgium

    M. Van Barel & A. Bultheel

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  1. M. Van Barel
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  2. A. Bultheel
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Van Barel, M., Bultheel, A. A general module theoretic framework for vector M-Padé and matrix rational interpolation. Numer Algor 3, 451–461 (1992). https://doi.org/10.1007/BF02141952

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  • DOI: https://doi.org/10.1007/BF02141952

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