双变量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 Double-Variable Linear Matrix Equation

作　　者：李书连[1] 张凯院[1] 武见[1] 

机构地区：[1]西北工业大学应用数学系,西安710072

出　　处：《工程数学学报》2012年第6期847-851,共5页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11071196)~~

摘　　要：通过构造等价的线性矩阵方程组(LMEs),将不相容的LMEs异类约束最小二乘解(Ls解)问题转化为相容的LMEs异类约束解问题,然后根据求LMEs的异类约束解的迭代算法构造原理,建立求LMEs的一种异类约束Ls解的迭代算法.不考虑舍入误差时,该算法可在有限步计算后求得LMEs的一组异类约束Ls解;选取特殊的初始矩阵时,该算法可求得LMEs的极小范数异类约束Ls解.此外,还可在LMEs的异类约束Ls解集合中给出指定矩阵的最佳逼近矩阵.For the incompatible LMEs, we first construct its equivalent linear matrix equations, and then change the corresponding different constrained least square solution problem into the different constrained solution problem of the compatible LMEs. Finally, an iterative method is designed to find the different constrained least square solution based on the structure principle of an iterative method for LMEs. With this iterative method, the different constrained least square solution can be obtained within finite iteration steps in the absence of round off errors, and the different constrained least square solution with least-norm can be obtained by choosing a special initial matrix. In addition, the optimal approximation matrix to any given matrix can be found under the framework of the different constrained least square solutions.

关 键 词：线性矩阵方程 异类约束最小二乘解 极小范数解 迭代算法 最佳逼近 

分 类 号：O241.6[理学—计算数学]