纺织高校基础科学学报2011，Vol.24Issue(3)：326-332,7.
多变量LME一种异类约束最小二乘解的迭代算法
An iterative method for different constrained least square solution of a multi-variables liner matrix equation
李书连 1张凯院1
作者信息
- 1. 西北工业大学应用数学系,陕西西安710072
- 折叠
摘要
Abstract
Based on the modified conjugate gradient method to find the different constrained solution of a multi-variables linear matrix equation, an iterative method is constructed to find the different constrained least square solution by constructing the equivalent linear matrix equations. Positive definiteness, reversibility and full column rank of the coefficient matrix of the equivalent linear matrix are not required for the iteration algorithm. So the iterative method is always feasibility. By this iterative method, the different constrained least square solutions can be obtained within finite iterative steps in the absence of round off errors, and the different constrained least square solution with least-norm can be got by choosing special initial matrix. In addition, the optimal approximation matrix to any given matrix can be obtained in the set of the different constrained least square solutions. The numerical examples show that the iterative method is efficient.关键词
多变量LME/异类约束最小二乘解/极小范数解/迭代算法/最佳逼近Key words
multi-variables liner matrix equation/different constrained least square solution/least-norm solution/ iterative method/ optimal approximation分类
数理科学引用本文复制引用
李书连,张凯院..多变量LME一种异类约束最小二乘解的迭代算法[J].纺织高校基础科学学报,2011,24(3):326-332,7.
