矩阵方程A^TXA=D的条件数与向后扰动分析

Condition Numberers and Backward Perturbation Analysis for the Matrix Equation A^TXA=D

讨论矩阵方程ATXA=D,该方程源于振动反问题和结构模型修正.本文利用Moore-Penrose广义逆的性质,给出该方程解的条件数的上、下界估计.同时,利用Schauder不动点理论给出该方程的向后扰动界,这些结果可用于该矩阵方程的数值计算.

This paper deals with the matrix equation ATXA=D, which arises in inverse problems in vibration and structural model updating. By using the properties of Moore-Penrose generalized inverse, the upper and lower bounds of the condition numbers associated with solving the matrix equation are presented. The backward perturbation bound for the matrix equation is given by using Schauder fixed-point theory. The results can be used in numerical solution for the matrix equation.