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Gröbner bases and generalized Padé approximation


Authors: Jeffrey B. Farr and Shuhong Gao
Journal: Math. Comp. 75 (2006), 461-473
MSC (2000): Primary 41A21, 13P10, 41A63
DOI: https://doi.org/10.1090/S0025-5718-05-01790-4
Published electronically: October 12, 2005
MathSciNet review: 2176409
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Abstract: It is shown how to find general multivariate Padé approximation using the Gröbner basis technique. This method is more flexible than previous approaches, and several examples are given to illustrate this advantage. When the number of variables is small compared to the degree of approximation, the Gröbner basis technique is more efficient than the linear algebra methods in the literature.


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Additional Information

Jeffrey B. Farr
Affiliation: Centre for Experimental and Constructive Mathematics (CECM) and Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6
Email: jfarr@cecm.sfu.ca

Shuhong Gao
Affiliation: Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634-0975
Email: sgao@ces.clemson.edu

DOI: https://doi.org/10.1090/S0025-5718-05-01790-4
Received by editor(s): February 10, 2004
Received by editor(s) in revised form: December 10, 2004
Published electronically: October 12, 2005
Additional Notes: This work was supported in part by the National Science Foundation (NSF) under Grant DMS0302549, the National Security Agency (NSA) under Grant MDA904-02-1-0067, and the DoD Multidisciplinary University Research Initiative (MURI) program administered by the Office of Naval Research (ONR) under Grant N00014-00-1-0565. MITACS also partially supported the first author.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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