Modular Algorithm for Sparse Multivariate Polynomial Interpolationand its Parallel Implementation

A new algorithm for sparse multivariate polynomial interpolation is presented. It is a multi-modular extension of the Ben-Or and Tiwari algorithm, and is designed to be a practical method to construct symbolic formulas from numeric data produced by vector or massively-parallel processors. The main i...

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Veröffentlicht in:Journal of Symbolic Computation Jg. 21; H. 4; S. 377 - 396
Hauptverfasser: MURAO, HIROKAZU, FUJISE, TETSURO
Format: Journal Article
Sprache:Englisch
Japanisch
Veröffentlicht: Elsevier Ltd 01.04.1996
Elsevier BV
Schlagworte:
Algebra and Number Theory
Computational Mathematics
ISSN:0747-7171, 1095-855X
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Abstract A new algorithm for sparse multivariate polynomial interpolation is presented. It is a multi-modular extension of the Ben-Or and Tiwari algorithm, and is designed to be a practical method to construct symbolic formulas from numeric data produced by vector or massively-parallel processors. The main idea in our algorithm comes from the well-known technique for primality test based on Fermat's theorem, and is the application of the generalized Chinese remainder theorem to the monomial exponents. We regard the exponent vector of each multivariate monomial as a mixed-radix representation of the corresponding exponent value obtained after the transformation by Kronecker's technique. It is shown by complexity comparison and experimental results that the step for univariate polynomial factorization is most expensive in our algorithm, and its parallelization is considered. Also reported are some empirical results of the parallelization on KLIC, a portable system of a concurrent logic programming language KL1.
AbstractList A new algorithm for sparse multivariate polynomial interpolation is presented. It is a multi-modular extension of the Ben-Or and Tiwari algorithm, and is designed to be a practical method to construct symbolic formulas from numeric data produced by vector or massively-parallel processors. The main idea in our algorithm comes from the well-known technique for primality test based on Fermat's theorem, and is the application of the generalized Chinese remainder theorem to the monomial exponents. We regard the exponent vector of each multivariate monomial as a mixed-radix representation of the corresponding exponent value obtained after the transformation by Kronecker's technique. It is shown by complexity comparison and experimental results that the step for univariate polynomial factorization is most expensive in our algorithm, and its parallelization is considered. Also reported are some empirical results of the parallelization on KLIC, a portable system of a concurrent logic programming language KL1.
Author MURAO, HIROKAZU
FUJISE, TETSURO
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crossref_primary_10_1016_j_jsc_2003_11_002
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Snippet A new algorithm for sparse multivariate polynomial interpolation is presented. It is a multi-modular extension of the Ben-Or and Tiwari algorithm, and is...
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StartPage 377
SubjectTerms Algebra and Number Theory
Computational Mathematics
Title Modular Algorithm for Sparse Multivariate Polynomial Interpolationand its Parallel Implementation
URI https://dx.doi.org/10.1006/jsco.1996.0020
https://cir.nii.ac.jp/crid/1872835442549904512
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