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线性流形上矩阵方程AX=B的一类反问题及数值解法
引用本文:廖安平.线性流形上矩阵方程AX=B的一类反问题及数值解法[J].计算数学,1998,20(4):371-376.
作者姓名:廖安平
作者单位:湖南师范大学数学系
摘    要:1.引言本文用*-"m表示全体nX。实矩阵的集合,人表示n阶单位矩阵,汉"m一《ME*""叫rank(川一r),**"""=HE*"""卜"A=v,**"""一仰E*"""卜"一M},SR;""(SR7"")表示全体7。阶实对称半正定(正定)阵集合.N(A)表示矩阵A的零空间,即N(A)=(xlAx=0),ID叫D表示Frobenius范数,A"表示矩阵A的Moors-Penrose广义逆,[EI十表示在Frobenius范数意义下n阶方阵E在SR;""中唯一的最佳k逼近解,即口一[E]+11-inf。。、。。x,IllE-All.([E]十求法见文[7]).还用A三0(A三0)表示A(的k阶顺序主子矩…

关 键 词:线性流形  最佳逼近  反问题  矩阵方程  数值解

A CLASS OF INVERSE PROBLEMS OF MATRIX EQUATION AX=B AND ITS NUMERICAL SOLUTION ON THE LINEAR MANIFOLD
Liao An-Ping.A CLASS OF INVERSE PROBLEMS OF MATRIX EQUATION AX=B AND ITS NUMERICAL SOLUTION ON THE LINEAR MANIFOLD[J].Mathematica Numerica Sinica,1998,20(4):371-376.
Authors:Liao An-Ping
Institution:Liao An-Ping (Department of Mathematics, Hunan Normal University)
Abstract:In this paper, a class of inverse problems of matrix equation AX=B is studied on the linear manifold, the necessary and sufficient conditions for the solvability of the inverse problem and the expression of the general solution are given; at the same time, the best approximation problem is considered, the expression of the best approximate solution and the numerical method are also given. This paper extends the results in 1, 2].
Keywords:linear manifold  best approximation  inverse problem  symmetric positive
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