摘要
讨论了如下两类问题 :问题 :给定 X∈ Rn× k,B∈ Rm× k,A0 ∈ Rp× q,求 A=A1 1 A1 2A2 1 A2 2∈ Rm× n使得 AX=B,A1 1 =A0 .问题 :给定 A*∈ Rm× n ,求 A∈ SA使得‖ A* - A‖ =minA∈ SA‖A* - A‖ .其中 SA是问题 的解集合 .给出了问题 有解的充分必要条件及解集合 SA 的一般形式 .对于问题 2 ,给出了解的表达式及一个数值算法与数值例子 .
In this paper,we consider the following two problems: Problem Ⅰ:Given X∈R n×k ,B∈R m×k ,A 0∈R p×q .find A=A 11 A 12 A 21 A 22 such that AX=B,A 11 =A 0. Problem Ⅱ:Given A * ∈R m×n ,find ∈S A such that ‖A *-‖=minA∈S A‖A -A‖. where is ‖·‖Frobenius norm and S A is the solution set of Problem Ⅰ. The necessary and sufficient conditions for the solvability of problem Ⅰ have been studied. The general form S A has been given. For problem Ⅱ,the expression of the solution has been presented, and an algorithm and a numerical example are given.
出处
《湖南农业大学学报（自然科学版）》
CAS
CSCD
北大核心
2001年第6期491-493,共3页
Journal of Hunan Agricultural University(Natural Sciences)
基金
国家自然科学基金资助项目 (198710 2 4)
