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矩阵方程AX=B的广义Hermite解及最佳逼近问题

发表时间:2009-01-15  浏览量:1862  下载量:806
全部作者: 梁茂林,马维学,王三福
作者单位: 天水师范学院数学与统计学院
摘 要: 矩阵P∈n×n满足P*=P+,则称之为广义酉矩阵;对广义酉矩阵P,若PAP=A*,则称A为广义Hermite矩阵。应用矩阵的奇异值分解,讨论了两类矩阵的结构。给定矩阵X,B∈n×m,得到矩阵方程AX=B 有广义Hermite解的充要条件,并给出有解时通解的表达式;同时考虑了给定矩阵的最佳逼近问题,并给出相应算法。
关 键 词: 数值代数;矩阵方程;广义酉矩阵;广义埃尔米特矩阵;奇异值分解;最佳逼近
Title: The generalized Hermite solutions of matrix equation AX=B and the optimal approximation problem
Author: LIANG Maolin, MA Weixue, WANG Sanfu
Organization: College of Mathematics and Statistics, Tianshui Normal University
Abstract: If matrix P∈n×n is satisfied with P*=P+, it can be called generalized unitary matrix. For generalized unitary matrix P, if PAP=A*, A can be called generalized Hermite matrix. Using singular value decomposition (SVD) of matrix, this paper discusses the structures of these two kinds of matrices. Given matrices X, B∈n×m, the necessary and sufficient conditions of matrix equation AX=B with generalized Hermite solutions are derived, the expression of general solution is given too. Meanwhile, the optimal approximation problem of the given matrix is considered, and the associated algorithm is given.
Key words: numerical algebra;matrix equation; generalized unitary matrix; generalized Hermite matrix; singular value decomposition; optimal approximation
发表期数: 2009年1月第1期
引用格式: 梁茂林,马维学,王三福. 矩阵方程AX=B的广义Hermite解及最佳逼近问题[J]. 中国科技论文在线精品论文,2009,2(1):100-104.
 
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