A BACKWARD STABLE ALGORITHM FOR QUADRATIC EIGENVALUE PROBLEMS

被引：16

作者：

Zeng, Linghui ^{[1
]}

Su, Yangfeng ^{[1
]}

机构：

[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China

来源：

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

关键词：

quadratic eigenvalue problem; eigenvalue condition number; backward error; stability; linearization; heavily damped; scaling; LINEARIZATIONS; ERROR;

D O I：

10.1137/130921234

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a backward stable algorithm for dense quadratic eigenvalue problems. Our algorithm incorporates a tropical-like scaling, a strategy for choosing linearizations, and an associated strategy for recovering eigentriples. We prove that the growth factor in the translation from conditioning for the quadratic to conditioning for the linearization and the growth factor in the translation from backward error for the linearization to backward error for the quadratic are both of order one in the algorithm.

引用

页码：499 / 516

页数：18

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