求解非线性矩阵方程X~α+A~*X^(-1)A=Q的免逆迭代算法  

Inverse-free iterative algorithm for nonlinear matrix equation X~α+A~*X^(-1)A=Q

作　　者：范广辉[1] 

机构地区：[1]曲阜师范大学数学科学学院

出　　处：《高师理科学刊》2014年第3期1-3,共3页Journal of Science of Teachers＇College and University

基　　金：国家自然科学基金资助项目(11171226);曲阜师范大学博士科研启动基金资助项目(20100102)

摘　　要：非线性矩阵方程Xα+A*X-1A=Q在工程中有着非常重要的应用,其中:A,Q为n维复矩阵,且Q为n维Hermitian正定矩阵.给出了当α≥1时,求解非线性矩阵方程Xα+A*X-1A=Q最大Hermitian正定解的免逆迭代算法,并通过数值举例说明了所给算法的有效性.Nonlinear matrix equation Xα＋A＊X-1A=Q , Hermitian positive definite, has widely applied background. where A , Q are n × n complex matrices with Q An inverse-free iterative algorithm for obtaining the maximal Hermitian positive definite solution of the above nonlinear matrix equation was proposed when a ≥ 1. And numerical example was given to show the efficiency of the proposed iterative method.

关 键 词：非线性矩阵方程 免逆迭代算法 最大解 

分 类 号：O241.6[理学—计算数学]