Multiplicity of zeros of algebraic system in eigenvalue method

被引：0

作者：

Zhang S. ^{[1
]}

Liu Y. ^{[1
]}

Feng G. ^{[1
]}

机构：

[1] Institute of Mathematics, Jilin University

来源：

Journal of Computer Science and Technology | 1999年 / 14卷 / 5期

关键词：

structure; algebraic system; eigenvalue method;

D O I：

10.1007/BF02948792

中图分类号：

学科分类号：

摘要：

This article deals with the structure relations between solutions to algebraic system and matrices in eigenvalue method for solving the algebraic system. The authors first discuss the condition on the ideal generated by the given system under which the eigenspace of matrix has dimension 1 since in this case the zero can be easily found. Then they study the relations between the multiplicity of zeros of the given system and orders of Jordan blocks of matrices formed in eigenvalue method.

引用

页码：510 / 517

页数：7

共 5 条

[1] Auzinger W., Stetter H.J., An elimination algorithm for the computation of all zeros of a system of multivariate polynomial equations, Conference in Numerical Analysis, pp. 11-30, (1988)
[2] Feng G., Zhang S., Reducing the multivariate polynomial system to eigenvalue problem, Northeastern Math. J., 8, 3, pp. 253-256, (1992)
[3] Feng G., Wu W., Zhang S., The eigenvalue problem equivalent to multivariate polynomial system, Numerical Mathematics, A J. of Chinese Universities, 2, 2, pp. 234-241, (1993)
[4] Moller H.M., Stetter H.J., Multivariate polynomial equations with multiple zeros solved by matrix eigen-problems, Numer. Math., 70, 3, pp. 311-329, (1995)
[5] Marinari M.G., Moller H.M., Mora T., Gröbner bases of ideals defined by functionals with an application to ideals of projective points, J. of AAECC, 4, pp. 103-145, (1993)

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