矩阵范数的应用——矩阵方程解的误差估计

Application of matrix norm on the error estimate of solution of matrix equation

设有矩阵方阵 AX=B,其中 A、B 是 n×n 的复矩阵,当 A、B 都有摄动矩阵或 A、B中的一个有摄动矩阵时,本文应用矩阵范数对矩阵方程 AX=B 的解的误差都作出估计。

In this paper,an estimation of error of solution of matrix equation is made,i.e., the following result is obtained. Theorem Let 1) δ=(δ_(ij))∈C^(n×n),δ(?)=(δ_(ij)(?))∈C^(n×n) be disturbance matrices of matrixA=(a_(ij)) ∈C^(n×n),B=(b_(ij))∈C^(n×n),respectively;2) A be an invertible matrix,B≠(0)_(n×n);3)‖A^(-1)δ‖<1, If there exist X.X(?) such that AX=B,(A+δ)X(?)=B+δ(?)=B(?) then:1(?) 2(?)