The resultant approach to computing vector characteristics of multiparameter polynomial matrices

被引：0

作者：

Khazanov V.B. ^{[1
]}

机构：

[1] St.Petersburg State Marine Technical University, St.Petersburg

来源：

Journal of Mathematical Sciences | 2006年 / 137卷 / 3期

基金：

俄罗斯基础研究基金会;

关键词：

Polynomial Matrix; Original Matrix; Polynomial Solution; Full Column Rank; Minimal Basis;

D O I：

10.1007/s10958-006-0284-6

中图分类号：

学科分类号：

摘要：

Known types of resultant matrices corresponding to one-parameter matrix polynomials are generalized to the multiparameter case. Based on the resultant approach suggested, methods for solving the following problems for multiparameter polynomial matrices are developed: computing a basis of the matrix range, computing a minimal basis of the right null-space, and constructing the Jordan chains and semilattices of vectors associated with a multiple spectrum point. In solving these problems, the original polynomial matrix is not transformed. Methods for solving other parametric problems of algebra can be developed on the basis of the method for computing a minimal basis of the null-space of a polynomial matrix. Issues concerning the optimality of computing the null-spaces of sparse resultant matrices and numerical precision are not considered. Bibliography: 19 titles. © 2006 Springer Science+Business Media, Inc.

引用

页码：4862 / 4878

页数：16

共 19 条

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[3]

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[7]

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[9]

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[10]

Khazanov V.B., On spectral properties of multiparameter polynomial matrices, Zap. Nauchn. Semin. POMI, 229, pp. 284-321, (1995)

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