標題: | Solving large-scale nonlinear matrix equations by doubling |
作者: | Weng, Peter Chang-Yi Chu, Eric King-Wah Kuo, Yueh-Cheng Lin, Wen-Wei 應用數學系 Department of Applied Mathematics |
關鍵字: | Doubling algorithm;Green's function;Krylov subspace;Leaky surface wave;Nano research;Nonlinear matrix equation;Surface acoustic wave |
公開日期: | 15-八月-2013 |
摘要: | We consider the solution of the large-scale nonlinear matrix equation X + BX-1 A - Q = 0, with A, B, Q, X is an element of C-nxn, and in some applications B = A(star) (star = T or H). The matrix Q is assumed to be nonsingular and sparse with its structure allowing the solution of the corresponding linear system Qv = r in O(n) computational complexity. Furthermore, B and A are respectively of ranks ra, rb << n. The type 2 structure-preserving doubling algorithm by Lin and Xu (2006) [241 is adapted, with the appropriate applications of the Sherman-Morrison-Woodbury formula and the lowrank updates of various iterates. Two resulting large-scale doubling algorithms have an O((r(a) + r(b))(3)) computational complexity per iteration, after some pre-processing of data in O(n) computational complexity and memory requirement, and converge quadratically. These are illustrated by the numerical examples. (C) 2012 Elsevier Inc. All rights reserved. |
URI: | http://dx.doi.org/10.1016/j.laa.2012.08.008 http://hdl.handle.net/11536/22116 |
ISSN: | 0024-3795 |
DOI: | 10.1016/j.laa.2012.08.008 |
期刊: | LINEAR ALGEBRA AND ITS APPLICATIONS |
Volume: | 439 |
Issue: | 4 |
起始頁: | 914 |
結束頁: | 932 |
顯示於類別: | 期刊論文 |