Division-free computation of subresultants using Bezout matrices

We present an algorithm to compute the subresultant sequence of two polynomials that completely avoids division in the ground domain, generalizing an algorithm given by Abdeljaoued et al. [J. Abdeljaoued, G. Diaz-Toca, and L. Gonzalez-Vega, Minors of Bezout matrices, subresultants and the parameteri...

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Vydáno v:International journal of computer mathematics Ročník 86; číslo 12; s. 2186 - 2200
Hlavní autor: Kerber, Michael
Médium: Journal Article
Jazyk:angličtina
Vydáno: Abingdon Taylor & Francis 01.12.2009
Taylor & Francis Ltd
Témata:
Algorithms
Bezout matrix
F.2.1 [Analysis of Algorithms and Problem Complexity]: Numerical Algorithms and Problems-Computations on Polynomials
I.1.2 [Symbolic and Algebraic Manipulation]: Algorithms-Algebraic algorithms
Mathematics
Matrix
polynomial gcd
Polynomials
subresultant
ISSN:0020-7160, 1029-0265
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Shrnutí:We present an algorithm to compute the subresultant sequence of two polynomials that completely avoids division in the ground domain, generalizing an algorithm given by Abdeljaoued et al. [J. Abdeljaoued, G. Diaz-Toca, and L. Gonzalez-Vega, Minors of Bezout matrices, subresultants and the parameterization of the degree of the polynomial greatest common divisor, Int. J. Comput. Math. 81 (2004), pp. 1223-1238]. We evaluate determinants of slightly manipulated Bezout matrices using the algorithm of Berkowitz. Although the algorithm gives worse complexity bounds than pseudo-division approaches, our experiments show that our approach is superior for input polynomials with moderate degrees if the ground domain contains indeterminates.
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ISSN:0020-7160
1029-0265
DOI:10.1080/00207160802460595