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H-bases for polynomial interpolation and system solving

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Abstract

The H-basis concept allows, similarly to the Gröbner basis concept, a reformulation of nonlinear problems in terms of linear algebra. We exhibit parallels of the two concepts, show properties of H-bases, discuss their construction and uniqueness questions, and prove that n polynomials in n variables are, under mild conditions, already H-bases. We apply H-bases to the solution of polynomial systems by the eigenmethod and to multivariate interpolation.

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Authors and Affiliations

  1. FB Mathematik der Universität Dortmund, D-44221, Dortmund, Germany E-mail:

    H. Michael Möller

  2. Mathematisches Institut, Universität Erlangen–Nürnberg, Bismarckstraße 1 1/2, D-91054, Erlangen, Germany E-mail:

    Thomas Sauer

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  1. H. Michael Möller
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  2. Thomas Sauer
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Möller, H.M., Sauer, T. H-bases for polynomial interpolation and system solving. Advances in Computational Mathematics 12, 335–362 (2000). https://doi.org/10.1023/A:1018937723499

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