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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| Veröffentlicht in: | International journal of computer mathematics Jg. 86; H. 12; S. 2186 - 2200 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Abingdon
Taylor & Francis
01.12.2009
Taylor & Francis Ltd |
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| ISSN: | 0020-7160, 1029-0265 |
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| Abstract | 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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| AbstractList | 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. [PUBLICATION ABSTRACT] 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. |
| Author | Kerber, Michael |
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| Cites_doi | 10.1016/S0304-3975(02)00639-4 10.1016/0020-0190(84)90018-8 10.1007/b102438 10.1214/aoms/1177731540 10.1016/S0747-7171(08)80013-2 10.1142/9789812791962_0003 10.1006/jsco.1999.0322 10.1006/jsco.2001.0462 10.1007/3-540-33099-2 10.1007/s00200-004-0158-4 10.1080/00207160412331284178 10.1145/321371.321381 10.1016/S0022-4049(98)00081-4 10.1016/S0019-9958(82)90766-5 |
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| References | Abdeljaoued J. (CIT0001) 2004 CIT0010 CIT0020 CIT0012 CIT0011 Chionh E. (CIT0007) 1999 Brown W. (CIT0006) 1971; 18 Kaltofen E. (CIT0015) 1989 Yap C. (CIT0021) 2000 Collins G. (CIT0009) 1967; 14 Basu S. (CIT0003) 2006 Loos R. (CIT0017) 1982 CIT0014 CIT0002 CIT0013 Rote G. (CIT0018) 2001; 2122 CIT0005 CIT0016 CIT0004 CIT0008 CIT0019 |
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| SubjectTerms | 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 |
| Title | Division-free computation of subresultants using Bezout matrices |
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