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The computation of non-perfect Padé-Hermite approximants

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Abstract

We describe a simple and efficient algorithm to generate a number of polynomial vectors which can be used to describe all possible solutions for a type I Padé-Hermite problem. If σ denotes the order of approximation, which is a measure for the size of the Padé-Hermite problem, it uses only order σ2 operations, even if the given system is not perfect. To this end, the problem is considered as a special case of a generalized Padé-Hermite problem which is also defined and analysed.

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

    Marc Van Barel & Adhemar Bultheel

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  1. Marc Van Barel
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  2. Adhemar Bultheel
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Communicated by J. Della Dora

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Van Barel, M., Bultheel, A. The computation of non-perfect Padé-Hermite approximants. Numer Algor 1, 285–304 (1991). https://doi.org/10.1007/BF02142327

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  • DOI: https://doi.org/10.1007/BF02142327

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