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

Hung Yuan Fan; Peter Chang Yi Weng; Eric King wah Chu

doi:10.1007/s10543-014-0469-1

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

Hung Yuan Fan
, Peter Chang Yi Weng
, Eric King wah Chu

數學系

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

4 引文斯高帕斯（Scopus）

摘要

We consider the refinement of estimates of invariant (or deflating) subspaces for a large and sparse real matrix (or pencil) in ℝ^n×n, 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 n, under appropriate assumptions, as illustrated by several numerical examples.

原文	英語
頁（從 - 到）	147-169
頁數	23
期刊	BIT Numerical Mathematics
卷	54
發行號	1
DOIs	https://doi.org/10.1007/s10543-014-0469-1
出版狀態	已發佈 - 2014 3月

ASJC Scopus subject areas

軟體
電腦網路與通信
計算數學
應用數學

存取文件

10.1007/s10543-014-0469-1

其它文件與鏈接

引用此

@article{a78e457369ed45369bdb3f3c19ec570c,

title = "Refining estimates of invariant and deflating subspaces for large and sparse matrices and pencils",

abstract = "We consider the refinement of estimates of invariant (or deflating) subspaces for a large and sparse real matrix (or pencil) in ℝn{\texttimes}n, 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 n, under appropriate assumptions, as illustrated by several numerical examples.",

keywords = "Deflating subspace, Invariant subspace, Large-scale problem, Newton's method, Nonsymmetric algebraic Riccati equation, Sparse matrix, Sylvester equation",

author = "Fan, \{Hung Yuan\} and Weng, \{Peter Chang Yi\} and Chu, \{Eric King wah\}",

note = "Funding Information: Acknowledgments The first author has been supported by the NSC, Taiwan Grant Number NSC 102-2115-M-003-009, and the second author by a Monash Graduate Scholarship and a Monash International Postgraduate Research Scholarship. Part of the work was completed when the third author visited the Shanghai Key Laboratory of Contemporary Applied Mathematics at FuDan University and National Taiwan Normal University.",

year = "2014",

month = mar,

doi = "10.1007/s10543-014-0469-1",

language = "English",

volume = "54",

pages = "147--169",

journal = "BIT Numerical Mathematics",

issn = "0006-3835",

publisher = "Springer Netherlands",

number = "1",

}

TY - JOUR

T1 - Refining estimates of invariant and deflating subspaces for large and sparse matrices and pencils

AU - Fan, Hung Yuan

AU - Weng, Peter Chang Yi

AU - Chu, Eric King wah

N1 - Funding Information: Acknowledgments The first author has been supported by the NSC, Taiwan Grant Number NSC 102-2115-M-003-009, and the second author by a Monash Graduate Scholarship and a Monash International Postgraduate Research Scholarship. Part of the work was completed when the third author visited the Shanghai Key Laboratory of Contemporary Applied Mathematics at FuDan University and National Taiwan Normal University.

PY - 2014/3

Y1 - 2014/3

N2 - We consider the refinement of estimates of invariant (or deflating) subspaces for a large and sparse real matrix (or pencil) in ℝn×n, 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 n, under appropriate assumptions, as illustrated by several numerical examples.

AB - We consider the refinement of estimates of invariant (or deflating) subspaces for a large and sparse real matrix (or pencil) in ℝn×n, 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 n, under appropriate assumptions, as illustrated by several numerical examples.

KW - Deflating subspace

KW - Invariant subspace

KW - Large-scale problem

KW - Newton's method

KW - Nonsymmetric algebraic Riccati equation

KW - Sparse matrix

KW - Sylvester equation

UR - https://www.scopus.com/pages/publications/84896394998

UR - https://www.scopus.com/pages/publications/84896394998#tab=citedBy

U2 - 10.1007/s10543-014-0469-1

DO - 10.1007/s10543-014-0469-1

M3 - Article

AN - SCOPUS:84896394998

SN - 0006-3835

VL - 54

SP - 147

EP - 169

JO - BIT Numerical Mathematics

JF - BIT Numerical Mathematics

IS - 1

ER -

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

摘要

ASJC Scopus subject areas

存取文件

其它文件與鏈接

指紋

引用此