摘要
利用两个Hermite正定矩阵的Thompson度量方法和闭凸集上单调算子不动点定理,给出非线性矩阵方程X-A^(*)(R+BXB^(*))^(-t)A=Q(0<t≤1)存在Hermite正定解的必要和充分条件,以及解的存在区间.建立求解该方程的迭代格式,并证明了迭代收敛性,同时应用Thompson度量和系数矩阵的特征值刻划了解的误差估计式.最后通过数值算例验证所给方法的有效性及可行性.
In this paper,by using the Thompson metric method of two Hermite positive definite matrices and thefixed point theorem of monotone operators on closed convex sets,we give some necessary and sufficient conditions for the existence of the Hermite positive definite solution of the nonlinear complex matrix equation X−A^(∗)(R+BX B^(∗))^(−t)A=Q(0<t≤1)and existence interval of the solution.The iterative scheme for solving the equation is established,and the iterative convergence is proved.In the meantime,the properties of the Thompson metric and the eigenvalue of the coefficient matrix are used to characterize the error estimation formula of the solution.Finally,the effectiveness and feasibility of the proposed method are verified by numerical examples.
作者
熊昊
黄敬频
张姗姗
XIONG Hao;HUANG Jing-pin;ZHANG Shan-shan(College of Mathematics and Physics,Guangxi University for Nationalities,Nanning 530006,China)
出处
《数学的实践与认识》
2022年第8期202-210,共9页
Mathematics in Practice and Theory
基金
国家自然科学基金(11661011)
广西民族大学研究生创新项目(gxun-chxps202071)。
作者简介
通信作者:黄敬频。
