矩阵不等式AX≥B的一类反问题及其最佳逼近

One Kind of Inverse Problem and Best Approximation for the Matrix Inequation AX≥B

讨论如下两个问题： 问题Ⅰ 给定非零向量Ｘ∈Ｒｎ，Ｂ∈Ｒｍ，求矩阵Ａ∈Ｒｍ×ｎ使得ＡＸ≥Ｂ． 问题Ⅱ 给定Ａ∈Ｒｍ×ｎ，求矩阵Ａ∈ＳＡ，使得 其中是Ｆｒｏｂｅｎｉｕｓ范数，ＳＡ表示问题Ⅰ的解集合。 给出了ＳＡ一般形式，对于问题Ⅱ，给出了解的表达式及一个数值例子。

In this paper, we discuss the following two problems: Problem Ⅰ Given nonzero vector X∈Rn, B∈ Rm, Find A∈Rm×n, such that AX≥B. Problem Ⅱ Given A∈Rm×n,Find A∈ SA,Such that where is Frobenius norm,and SA is the solution set of Problem Ⅰ The general form of SA has been given. For Problem Ⅱ， the express of the solution and one numerical examples has been provided.