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Gröbner bases, H-bases and interpolation


Author: Thomas Sauer
Journal: Trans. Amer. Math. Soc. 353 (2001), 2293-2308
MSC (2000): Primary 65D05, 12Y05; Secondary 65H10
DOI: https://doi.org/10.1090/S0002-9947-00-02646-5
Published electronically: October 11, 2000
MathSciNet review: 1814071
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Abstract:

The paper is concerned with a construction for H-bases of polynomial ideals without relying on term orders. The main ingredient is a homogeneous reduction algorithm which orthogonalizes leading terms instead of completely canceling them. This allows for an extension of Buchberger's algorithm to construct these H-bases algorithmically. In addition, the close connection of this approach to minimal degree interpolation, and in particular to the least interpolation scheme due to de Boor and Ron, is pointed out.


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Additional Information

Thomas Sauer
Affiliation: Mathematisches Institut, Universität Erlangen–Nürmberg, Bismarckstr. $1 \frac12$, D–91054 Erlangen, Germany
Address at time of publication: Justus-Liebig-Universität Gießen, Lehrstuhl für Numerische Mathematik Heinrich-Buff-Ring 44, D-35392 Gießen, Germany
Email: sauer@mi.uni-erlangen.de

DOI: https://doi.org/10.1090/S0002-9947-00-02646-5
Keywords: H--bases, reduction algorithm, interpolation
Received by editor(s): March 11, 1999
Received by editor(s) in revised form: July 12, 1999
Published electronically: October 11, 2000
Additional Notes: Supported by a Heisenberg fellowship from Deutsche Forschungsgemeinschaft, Grant Sa 627/6.
Article copyright: © Copyright 2000 American Mathematical Society

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