期刊论文详细信息
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 卷:315
Projected nonsymmetric algebraic Riccati equations and refining estimates of invariant and deflating subspaces
Article
Fan, Hung-Yuan1  Chu, Eric King-wah2 
[1] Natl Taiwan Normal Univ, Dept Math, Taipei 116, Taiwan
[2] Monash Univ, Sch Math Sci, Bldg 28, Clayton, Vic 3800, Australia
关键词: Deflating subspace;    Invariant subspace;    Large-scale problem;    Nonsymmetric algebraic Riccati equation;    Sparse matrix;    Sylvester equation;   
DOI  :  10.1016/j.cam.2016.10.018
来源: Elsevier
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【 摘 要 】

We consider the numerical solution of the projected nonsymmetric algebraic Riccati equations or their associated Sylvester equations via Newton's method, arising in the refinement of estimates of invariant (or deflating subspaces) for a large and sparse real matrix A (or pencil A AB). The engine of the method is the inversion of the matrix P(2)P(2)(T)A - gamma I-n or Pl2Pl2T (A - gamma B), for some orthonormal P-2 or P-l2 from R-nx(n m), making use of the structures in A or A - lambda B and the Sherman-Morrison-Woodbury formula. Our algorithms are efficient, under appropriate assumptions, as shown in our error analysis and illustrated by numerical examples. (C) 2016 Elsevier B.V. All rights reserved.

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