中文摘要：

为了求解非线性矩阵方程Xs＋∑i=1AHiX-tiAi=Q在0〈s≤1，t≥1时的最大Hermitian正定解，运用不动点迭代算法和矩阵理论知识，给出了解存在的条件以及算法的收敛性证明。

英文摘要：

In order to solve the maximal Hermitian positive definite solution of nonlinear matrix equationXs＋∑i=1AHiX-tiAi=Q（0 〈 s ≤ 1, t ≥ 1）, the existence condition of positive definite solution for the matrix equation is derived by fixed-point it-eration algorithm and matrix decomposition, and the conversation of the algorithm is proved.