MINIMIZATION OF THE NORM, THE NORM OF THE INVERSE AND THE CONDITION NUMBER OF A MATRIX BY COMPLETION

被引：7

作者：

ELSNER, L ^{[1
]}

HE, CY ^{[1
]}

MEHRMANN, V ^{[1
]}

机构：

[1] TECH UNIV CHEMNITZ ZWICKAU,FAK MATH,D-09107 CHEMNITZ,GERMANY

来源：

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS | 1995年 / 2卷 / 02期

关键词：

CONDITION NUMBER; NORM OF A MATRIX; MATRIX COMPLETION; DILATION THEORY; ROBUST REGULARIZATION OF DESCRIPTOR SYSTEMS;

D O I：

10.1002/nla.1680020207

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the problem of minimizing the norm, the norm of the inverse and the condition number with respect to the spectral norm, when a submatrix of a matrix can be chosen arbitrarily. For the norm minimization problem we give a different proof than that given by Davis/Kahan/Weinberger. This new approach can then also be used to characterize the completions that minimize the norm of the inverse. For the problem of optimizing the condition number we give a partial result.

引用

页码：155 / 171

页数：17

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