计算数学 2002, 24(2) 165-176 DOI:     ISSN: 0254-7791 CN: 11-2125/O1

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PubMed

用矩阵分解求解线性矩阵方程的最优解

袁永新

华东船舶工业学院 镇江,212003

摘要

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THE OPTIMAL SOLUTION OF LINEAR MATRIX EQUATIONS BY MATRIX DECOMPOSITIONS

Yuan Yongxin (East China Shipbuilding Institute, Zhenjiang, 212003)

Abstract:

In this paper, the following problems are considered Problem I. Given A ∈Rm×n, D ∈ R n×n. a) Let S1 = {X: X ∈ Rm×n, ||ATX - XTA - D|| = min} find X ∈ S1 such that ||X|| = min; b) Let S2 = {X: X ∈ Rm×n, ATX - XTA = D} find X ∈ S2 such that ||X|| = min. Problem II. Given A ∈ Rm×n,B B∈Rn×p, D ∈Rm×p. Let L1 = {X: X ∈ SRn×n, AXB = D} find X ∈ L1 such that ||X|| = min. Problem III. Given A ∈ Rm×n,B ∈ Rp×q, C ∈ Rm×q, G ∈ Rl×n, H ∈ Rp×t,D ∈ Rl × t. Let L2 = {X: X ∈ Rn×p, AXB = C, GXH = D} find X ∈ L2 such that ||X|| = min. Using singularvalue and canonical correlation decompositions, the necessary and sufficiellt conditions, under which S2, L1 and L2 are nonempty, are studied. The expressions for the solutions of Problems I, II and III are given.

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收稿日期  修回日期  网络版发布日期 2002-02-14 00:00:00.0 
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