一类非线性矩阵方程组的Hermite正定解

The Hermite positive definite solution of a system of nonlinear matrix equations

研究了一类非线性矩阵方程组的Hermite正定解求解问题.证明了矩阵方程组Hermite正定解的存在性并给出取值范围,构造出求解矩阵方程组的迭代方法并利用单调有界定理证明其收敛性,然后对其Hermite正定解进行扰动分析并给出扰动上界.最后运用数值算例说明所给方法的有效性及可行性.

The problem of solving the Hermite positive definite solution for the system of nonlinear matrix equations is studied.Firstly,the existence of the Hermite positive definite solution of the system of matrix equations is proven,and the range of values is given.An iterative method for solving the system of matrix equations is constructed,and its convergence is proved by the monotone bounded theorem.Furthermore,the perturbation analysis is discussed and the erturbation upper bound is derived.Finally,numerical examples are given to illustrate the effectiveness and feasibility of the proposed iterative method.