矩阵方程的秩约束最小二乘对称半正定解及其最佳逼近  

Rank Constraint Least Square Symmetric Semidefinite Solutions and Its Optimal Approximation of the Matrix Equation

作　　者：喻思婷 彭靖静[1] 彭振赟[1] YU Siting;PENG Jingjing;PENG Zhenyun(College of Mathematics and Computer Science,Guilin University of Electronic Technology,Guilin Guangxi 541004,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《广西师范大学学报（自然科学版）》2022年第4期136-144,共9页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(11961012);广西自然科学基金(2018GXNSFBA281192);广西科技基地和人才专项项目(AD20297063)。

摘　　要：基于矩阵的奇异值分解和对称矩阵谱分解,给出矩阵方程AX=B有秩约束最小二乘对称半正定解及其最佳逼近解的充分必要条件及有解时解的一般表达式;给出求解最佳逼近解的计算步骤;用数值例子说明结果的正确性。Based on the singular value decomposition and spectral decomposition of matrices,the necessary and sufficient conditions for the existence of solutions to rank constraint least square symmetric semidefinite solutions and itsoptimal approximation solution of the matrix equation AX=B are established and,if the solutions exist,the general expression of the solutions are proposed.The computational procedures of the optimal approximation solution,and the numerical examples showing the correctness of the theoretical results are given.

关 键 词：秩约束矩阵 矩阵方程 对称半正定矩阵 最小二乘解 最佳逼近 

分 类 号：O151.21[理学—数学]