A geometric approach to perturbation theory of matrices and matrix pencils .1. Versal deformations

被引：69

作者：

Edelman, A ^{[1
]}

Elmroth, E ^{[1
]}

Kagstrom, B ^{[1
]}

机构：

[1] UMEA UNIV, DEPT COMP SCI, S-90187 UMEA, SWEDEN

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 1997年 / 18卷 / 03期

关键词：

Jordan canonical form; Kronecker canonical form; generalized Schur decomposition; staircase algorithm; versal deformations; tangent and normal spaces; singularity theory; perturbation theory;

D O I：

10.1137/S0895479895284634

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive versal deformations of the Kronecker canonical form by deriving the tangent space and orthogonal bases for the normal space to the orbits of strictly equivalent matrix pencils. These deformations reveal the local perturbation theory of matrix pencils related to the Kronecker canonical form. We also obtain a new singular value bound for the distance to the orbits of less generic pencils. The concepts, results, and their derivations are mainly expressed in the language of numerical linear algebra. We conclude with experiments and applications.

引用

页码：653 / 692

页数：40

共 37 条

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[Anonymous], 1976, SINGULARITY THEORY I

[2]

Arnold V.I., 1971, R. Math. Surveys, V26, P29

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