【摘要】 基于正规锥上单调算子的不动点定理,本文研究非线性矩阵方程X-(sum from i=1 to m) A_i*X~δA_i=Q的正定解。给出了正定解的存在性定理,并且构造了求解的m步定常迭代方法,最后证明了该迭代法的收敛性。更多还原

【Abstract】 Based on the monotone operator fixed point theorem in normal cone,the positive definite solution of the nonlinear matrix equation X-(sum from i=1 to m) A_i*X~δA_i=Q is investigated. The existence theorem for a unique positive definite solution is given. A sort of m-step stationary iterative method is proposed to compute the unique positive definite solution and its convergence is proved.更多还原