BOUNDS ON PERTURBATIONS OF GENERALIZED SINGULAR-VALUES AND OF ASSOCIATED SUBSPACES

被引：16

作者：

LI, RC ^{[1
]}

机构：

[1] INST APPL PHYS & COMP MATH,BEIJING 100088,PEOPLES R CHINA

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 1993年 / 14卷 / 01期

关键词：

GRASSMANN MATRIX PAIR; GENERALIZED SINGULAR VALUE DECOMPOSITION; GENERALIZED SINGULAR SUBSPACE; THE CHORDAL METRIC; METRICS ON GRASSMANN MANIFOLD; UNITARILY INVARIANT NORM; PERTURBATION BOUND;

D O I：

10.1137/0614017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The sensitivity of the generalized singular value decomposition of a matrix pair to perturbations in the matrix elements is analysed. It is shown how the chordal distances between the singular values and the angular distance between the generalized singular spaces can be bounded in terms of the angular distances between the matrices. The main results are generalizations of several results on the standard singular value problem.

引用

页码：195 / 234

页数：40

共 50 条

[1] BOUNDS FOR THE SINGULAR-VALUES OF A MATRIX
JENNINGS, A
[J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 1982, 2 (04) : 459 - 474
[2] BOUNDS FOR SINGULAR-VALUES BASED ON THE EIGENVECTORS
COHEN, N
LEWKOWICZ, I
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1991, 149 : 227 - 248
[3] BOUNDS FOR SINGULAR-VALUES USING TRACES
MERIKOSKI, JK
SARRIA, H
TARAZAGA, P
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1994, 210 : 227 - 254
[4] BOUNDS ON GENERALIZED STRUCTURED SINGULAR-VALUES VIA THE PERRON ROOT OF MATRIX MAJORANTS
CHEN, J
NETT, CN
[J]. SYSTEMS & CONTROL LETTERS, 1992, 19 (06) : 439 - 449
[5] LENGTH BOUNDS FOR SINGULAR-VALUES OF SPARSE MATRICES
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NYLEN, PM
[J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 1993, 14 (04) : 1043 - 1047
[6] GENERALIZED SINGULAR-VALUES AND INTERLACING INEQUALITIES
WIMMER, HK
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1989, 137 (01) : 181 - 184
[7] YAMAMOTO THEOREM FOR GENERALIZED SINGULAR-VALUES
JOHNSON, CR
NYLEN, P
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1990, 128 : 147 - 158
[8] BOUNDS FOR THE SINGULAR-VALUES OF BLOCK COMPANION MATRICES
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VITORIA, J
[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1992, 170 : 225 - 228
[9] INTERLACING INEQUALITIES FOR GENERALIZED SINGULAR-VALUES
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[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1987, 87 : 85 - 92
[10] BOUNDS FOR THE SINGULAR-VALUES OF A MATRIX WITH NONNEGATIVE EIGENVALUES
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[J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 1989, 112 : 29 - 37

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