Stability analysis of block LDLT factorization for symmetric indefinite matrices

被引：6

作者：

Fang, Haw-ren ^{[1
]}

机构：

[1] Univ Minnesota, Dept Comp Sci & Engn, Minneapolis, MN 55455 USA

来源：

IMA JOURNAL OF NUMERICAL ANALYSIS | 2011年 / 31卷 / 02期

基金：

美国国家科学基金会;

关键词：

backward error analysis; numerical stability; block LDLT factorization; symmetric indefinite matrix; inertia preservation; inertia estimation; rank estimation; TRIDIAGONAL MATRICES; PIVOTING STRATEGY; LINEAR-EQUATIONS; SYSTEMS;

D O I：

10.1093/imanum/drp053

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider block LDLT factorization for symmetric indefinite matrices in the form LDLT, where L is unit lower triangular and D is block diagonal with each diagonal block having dimension 1 or 2. The stability of this factorization and its application to solving symmetric indefinite linear systems has been well studied. On the other hand, while all rounding error analysis of block LDLT factorization in the literature relies on the outer product form, this paper gives a novel componentwise backward error analysis based on the inner product form. The new results include a condition under which block LDLT factorization in inexact arithmetic is guaranteed to preserve the inertia and a reliability analysis of rank estimation and inertia estimation of symmetric indefinite matrices by block LDLT factorization.

引用

页码：528 / 555

页数：28