西北师范大学学报（自然科学版）Issue(6)：20-25,6.
多变量矩阵方程的对称最小二乘解及其最佳逼近
The least squares symmetric solutions of the matrix equation with several variables and its optimal approximation
摘要
Abstract
The least squares symmetric solutions of the matrix equation with several variables are too difficult to be obtained by applying matrices decomposition.An iterative method is presented to solve the least squares symmetric solutions of the linear matrix equation and its convergence is proved. And minimum norm of the least squares symmetric solutions can be obtained by choosing a special kind of initial symmetric matrices.In addition, the unique optimal approximation solutions to the given matrices in Frobenius norm can be obtained.The given numerical examples demonstrate that the iterative methods are quite efficient.关键词
矩阵方程/对称最小二乘解组/极小范数解组/最佳逼近解组Key words
matrix equation/least squares symmetric solution group/least norm solution group/optimal approximation solution group分类
数理科学引用本文复制引用
刘莉,王伟..多变量矩阵方程的对称最小二乘解及其最佳逼近[J].西北师范大学学报（自然科学版）,2014,(6):20-25,6.基金项目
国家自然科学基金资助项目(11201253) （11201253）
