Refining estimates of invariant and deflating subspaces for large and sparse matrices and pencils

被引：4

作者：

Fan, Hung-Yuan ^{[1
]}

Weng, Peter Chang-Yi ^{[2
]}

Chu, Eric King-wah ^{[2
]}

机构：

[1] Natl Taiwan Normal Univ, Dept Math, Taipei 116, Taiwan

[2] Monash Univ, Sch Math Sci, Clayton, Vic 3800, Australia

来源：

BIT NUMERICAL MATHEMATICS | 2014年 / 54卷 / 01期

关键词：

Deflating subspace; Invariant subspace; Large-scale problem; Newton's method; Nonsymmetric algebraic Riccati equation; Sparse matrix; Sylvester equation; CONTINUATION; ALGORITHM; EQUATIONS;

D O I：

10.1007/s10543-014-0469-1

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

We consider the refinement of estimates of invariant (or deflating) subspaces for a large and sparse real matrix (or pencil) in , through some (generalized) nonsymmetric algebraic Riccati equations or their associated (generalized) Sylvester equations via Newton's method. The crux of the method is the inversion of some well-conditioned unstructured matrices via the efficient and stable inversion of the associated structured but near-singular matrices. All computations have complexity proportional to , under appropriate assumptions, as illustrated by several numerical examples.

引用

页码：147 / 169

页数：23

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