標題: | Complex symmetric stabilizing solution of the matrix equation X plus A(T)X(-1)A = Q |
作者: | Guo, Chun-Hua Kuo, Yueh-Cheng Lin, Wen-Wei 數學建模與科學計算所(含中心) Graduate Program of Mathematical Modeling and Scientific Computing, Department of Applied Mathematics |
關鍵字: | Nonlinear matrix equation;Complex symmetric solution;Stabilizing solution;Doubling algorithm |
公開日期: | 15-九月-2011 |
摘要: | We study the matrix equation X + A(T)X(-1)A = Q, where A is a complex square matrix and Q is complex symmetric. Special cases of this equation appear in Green's function calculation in nano research and also in the vibration analysis of fast trains. In those applications, the existence of a unique complex symmetric stabilizing solution has been proved using advanced results on linear operators. The stabilizing solution is the solution of practical interest. In this paper we provide an elementary proof of the existence for the general matrix equation, under an assumption that is satisfied for the two special applications. Moreover, our new approach here reveals that the unique complex symmetric stabilizing solution has a positive definite imaginary part. The unique stabilizing solution can be computed efficiently by the doubling algorithm. (C) 2011 Elsevier Inc. All rights reserved. |
URI: | http://dx.doi.org/10.1016/j.laa.2011.03.034 http://hdl.handle.net/11536/19193 |
ISSN: | 0024-3795 |
DOI: | 10.1016/j.laa.2011.03.034 |
期刊: | LINEAR ALGEBRA AND ITS APPLICATIONS |
Volume: | 435 |
Issue: | 6 |
起始頁: | 1187 |
結束頁: | 1192 |
顯示於類別: | 期刊論文 |