矩阵方程X+A^(*)X^(-2)A=I极大解的扰动分析

Perturbation analysis of the maximal solution of the Matrix equations X+A^(*)X^(-2)A=I

考虑非线性矩阵方程X+A^(*)X^(-2)A=I,其中A是n阶复矩阵,I是n阶单位矩阵.通过初等微积分推导出此方程极大解的新扰动界,并给出数值例子对所得结果与已有结果进行比较说明.

In this paper,the nonlinear matrix equations X+A^(*)X^(-2)A=I is discussed,where A is an n×n complex matrix and I is an n×n identity matrix.Besides,a new perturbation bound for maximal solution of this equation is derived by elementary calculus.Meanwhile,a numerical example is given to compare the obtained results with the existing ones.