On equations that are equivalent to the nonlinear matrix equation X plus A*X-α A = Q

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:234

Article

Wang, Xing Tao¹  Li, Yuan Min¹ 

[1] Harbin Inst Technol, Dept Math, Harbin 150001, Peoples R China

关键词: Nonlinear matrix equation;    Iterative algorithm;    Positive definite solution;   

DOI  :  10.1016/j.cam.2010.03.004

来源: Elsevier

【 摘 要 】

The nonlinear matrix equation X-1 + A*X(alpha)A = Q (0 < alpha <= 1) is equivalent to the nonlinear matrix equation X + A*X(-alpha)A = Q (0 < alpha <= 1). The nonlinear matrix equation X-1 + (AXA*)(1/alpha) = Q (1 < alpha) is equivalent to the nonlinear matrix equation X-1 + A*X(alpha)A = Q (1 < alpha). The necessary and sufficient conditions for the existence of a positive definite solution of X-1 + A*X(alpha)A = Q (0 < alpha <= 1) and X-1 + (AXA*)(1/alpha) = Q (1 < alpha) are given. In the process, two iterative algorithms are obtained. Estimations of the errors of the iterative algorithms are derived. Two numerical examples are given that demonstrate that the iterative algorithms are applicable. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

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