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A uniform approach for Hermite Padé and simultaneous Padé approximants and their matrix-type generalizations

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Abstract

This paper introduces the notion of apower Hermite Padé approximant, a generalization of the classical scalar Hermite Padé approximant. We show that this generalized form provides a unifor approach for different concepts of matrix-type Padé approximants. This includes descriptions of vector and matrix Padé approximants along with generalizations of simultaneous and Hermite Padé approximants.

A complete description of these new approximants, based on the characterization of a corresponding linear solution space, is given. A Padé-like table is introduced and the singular structure is studied. It is shown that the geometric structure of the singular blocks of this new table is made up of one or more combinations of triangles. In the special case of matrix Padé approximants the geometric structure of the combined singular areas consists of square blocks — exactly the same as in the classical scalar Padé case.

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Authors and Affiliations

  1. Institut für Angewandte Mathematik, Universität Hannover, Welfengarten 1, W-3000, Hannover, Germany

    Bernhard Beckermann

  2. Department of Computing Science, University of Waterloo, Waterloo, Ontario, Canada

    George Labahn

Authors
  1. Bernhard Beckermann
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  2. George Labahn
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Beckermann, B., Labahn, G. A uniform approach for Hermite Padé and simultaneous Padé approximants and their matrix-type generalizations. Numer Algor 3, 45–54 (1992). https://doi.org/10.1007/BF02141914

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  • DOI: https://doi.org/10.1007/BF02141914

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