中北大学学报（自然科学版）2012，Vol.33Issue(4)：358-362,386,6.DOI:10.3969/j.issn.1673-3193.2012.04.002
求双变量LME一种异类约束最小二乘解的MCG算法
Modified Conjugate Gradient Method for a Different Constrained Least Square Solution of Two-Variables Linear Matrix Equation
摘要
Abstract
Based on the modified conjugate gradient method, which gets same constrained least square solution of the linear matrix equation, a modified conjugate gradient method is constructed for different constrained least square solution of the linear matrix equation with two variables.And the convergence of this method is proved.By this method, a different constrained least square solution can be obtained within finite iterative steps in absence of round-off errors, and the different constrained least square solution with least-norm can be got by choosing special initial matrices.In addition, the optimal approximation matrix to any given matrix can be obtained in the set of the different constrained least square solutions. Examples show the efficiency of the method.关键词
线性矩阵方程/异类约束最小二乘解/修正共轭梯度法/极小范数解/最佳逼近Key words
linear matrix equation/ different constrained least square solution/ modified conjugate gradient method/ least-norm solution/ optimal approximation分类
数理科学引用本文复制引用
刘晓敏,张凯院,谢培月..求双变量LME一种异类约束最小二乘解的MCG算法[J].中北大学学报（自然科学版）,2012,33(4):358-362,386,6.基金项目
国家自然科学基金资助项目(11071196) （11071196）
