ON A PERTURBATION BOUND FOR INVARIANT SUBSPACES OF MATRICES

被引：15

作者：

Karow, Michael ^{[1
]}

Kressner, Daniel ^{[2
]}

机构：

[1] Tech Univ Berlin, Inst Math, D-10623 Berlin, Germany

[2] Ecole Polytech Fed Lausanne, MATHICSE, CH-1015 Lausanne, Switzerland

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 2014年 / 35卷 / 02期

关键词：

invariant subspaces; perturbation theory; pseudospectra; quadratic matrix equation; STABLE EIGENDECOMPOSITIONS; SEPARATION; ERROR;

D O I：

10.1137/130912372

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Given a nonsymmetric matrix A, we investigate the effect of perturbations on an invariant subspace of A. The result derived in this paper differs from Stewart's classical result and sometimes yields tighter bounds. Moreover, we provide norm estimates for the remainder terms in well-known perturbation expansions for invariant subspaces, eigenvectors, and eigenvalues.

引用

页码：599 / 618

页数：20

共 50 条

[41] Algorithms for computating principal and minor invariant subspaces of large matrices
Hasan, MA
PROCEEDINGS OF THE 2003 IEEE INTERNATIONAL SYMPOSIUM ON CIRCUITS AND SYSTEMS, VOL V: BIO-MEDICAL CIRCUITS & SYSTEMS, VLSI SYSTEMS & APPLICATIONS, NEURAL NETWORKS & SYSTEMS, 2003, : 669 - 672
[42] Fast parallelizable methods for computing invariant subspaces of Hermitian matrices
Zhang, Zhenyue
Zha, Hongyuan
Ying, Wenlong
JOURNAL OF COMPUTATIONAL MATHEMATICS, 2007, 25 (05) : 583 - 594
[43] Subscalarity, Invariant, and Hyperinvariant Subspaces for Upper Triangular Operator Matrices
Salah Mecheri
Bulletin of the Malaysian Mathematical Sciences Society, 2018, 41 : 1085 - 1104
[44] Rational Procedures in the Problem of Common Invariant Subspaces of Two Matrices
Yu. A. Al'pin
Kh. D. Ikramov
Journal of Mathematical Sciences, 2003, 114 (6) : 1757 - 1764
[45] Simple forms and invariant subspaces of H-expansive matrices
Fourie, J. H.
Groenewald, G. J.
van Rensburg, D. B. Janse
Ran, A. C. M.
LINEAR ALGEBRA AND ITS APPLICATIONS, 2015, 470 : 300 - 340
[46] Hyponormal matrices and semidefinite invariant subspaces in indefinite inner products
Mehl, C
Ran, ACM
Rodman, L
ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2004, 11 : 192 - 204
[47] NONSINGULAR FACTORS OF POLYNOMIAL-MATRICES AND (A,B)-INVARIANT SUBSPACES
EMRE, E
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1980, 18 (03) : 288 - 296
[48] On a functional approach to constructing projections onto invariant subspaces of matrices
Demidenko, GV
SIBERIAN MATHEMATICAL JOURNAL, 1998, 39 (04) : 683 - 699
[49] On a functional approach to constructing projections onto invariant subspaces of matrices
G. V. Demidenko
Siberian Mathematical Journal, 1998, 39 : 683 - 699
[50] Stability of Invariant Subspaces of Real Tri-diagonal Matrices
Xu, Guanghui
Xu, Changqqing
ADVANCES IN MATRIX THEORY AND ITS APPLICATIONS, VOL II: PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON MATRIX THEORY AND ITS APPLICATIONS, 2008, : 371 - 374

← 1 2 3 4 5 →