| THE EIGENVALUE PROBLEM EQUIVALENT TO MULTIVARIATE POLYNOMIAL SYSTEM |
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| 引用本文： | 冯果忱,吴文达,张树功. THE EIGENVALUE PROBLEM EQUIVALENT TO MULTIVARIATE POLYNOMIAL SYSTEM[J]. 高等学校计算数学学报(英文版), 1993, 0(2) |
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| 作者姓名： | 冯果忱 吴文达 张树功 |
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| 作者单位： | Institute of Mathematics，Jilin University，Changchun 130023，PRC.，Beijing Municipal Computer Center，Beijing 100000.PRC.，Institute of Mathematics，Jilin University，Chang chun，130023，PRC. |
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| 摘 要： | In this paper, the authors proved that finding all solutions of a given multivariate polynomial system is equivalent to solving a relative joint eigenvalue problem(Theorem 1) and in some cases one can find all solutions of the given system from the eigenvalues and vectors of one matrix or matrix pencil (Theorem 2). Especially the situation that the ideal generated by the given system is 0-dimensional is discussed.
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THE EIGENVALUE PROBLEM EQUIVALENT TO MULTIVARIATE POLYNOMIAL SYSTEM |
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| Feng Guo-chen Institute of Mathematics,Jilin University,Changchun ,PRC. Wu Wen-da Beijing Municipal Computer Center,Beijing .PRC. Zhang Shu-gong Institute of Mathematics,Jilin University,Chang chun,,PRC.. THE EIGENVALUE PROBLEM EQUIVALENT TO MULTIVARIATE POLYNOMIAL SYSTEM[J]. Numerical Mathematics A Journal of Chinese Universities English Series, 1993, 0(2) |
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| Authors: | Feng Guo-chen Institute of Mathematics Jilin University Changchun PRC. Wu Wen-da Beijing Municipal Computer Center Beijing .PRC. Zhang Shu-gong Institute of Mathematics Jilin University Chang chun PRC. |
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| Affiliation: | Feng Guo-chen Institute of Mathematics,Jilin University,Changchun 130023,PRC. Wu Wen-da Beijing Municipal Computer Center,Beijing 100000.PRC. Zhang Shu-gong Institute of Mathematics,Jilin University,Chang chun,130023,PRC. |
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| Abstract: | In this paper, the authors proved that finding all solutions of a given multivariate polynomial system is equivalent to solving a relative joint eigenvalue problem(Theorem 1) and in some cases one can find all solutions of the given system from the eigenvalues and vectors of one matrix or matrix pencil (Theorem 2). Especially the situation that the ideal generated by the given system is 0-dimensional is discussed. |
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| Keywords: | Polynomial system equivalent joint eigenvalue problem 0-dimensional ideal. |
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