PROBABILISTIC BOUNDS ON THE EXTREMAL EIGENVALUES AND CONDITION NUMBER BY THE LANCZOS-ALGORITHM

被引：21

作者：

KUCZYNSKI, J ^{[1
]}

WOZNIAKOWSKI, H ^{[1
]}

机构：

[1] COLUMBIA UNIV,INST APPL MATH,NEW YORK,NY 10027

来源：

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS | 1994年 / 15卷 / 02期

关键词：

EXTREME EIGENVALUES; LANCZOS ALGORITHM; CONDITION NUMBER; RANDOM START;

D O I：

10.1137/S0895479892230456

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The authors analyze the Lanczos algorithm with a random start for approximating the extremal eigenvalues of a symmetric positive definite matrix. They present some bounds on the Lebesgue measure (probability) of the sets of these starting vectors for which the Lanczos algorithm gives at the kth step satisfactory approximations to the largest and smallest eigenvalues. Combining these bounds gets similar estimates for the condition number of a matrix.

引用

页码：672 / 691

页数：20

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