特殊双变量矩阵方程组异类约束解的MCG算法  

MCG METHOD TO FIND DIFFERENT CONSTRAINED SOLUTION OF SPECIAL DOUBLE-VARIABLE MATRIX EQUATIONS

作　　者：解培月[1] 张凯院[1] 

机构地区：[1]西北工业大学应用数学系,陕西西安710072

出　　处：《数学杂志》2012年第4期649-657,共9页Journal of Mathematics

基　　金：国家自然科学基金(11071196)

摘　　要：本文研究了约束矩阵方程问题中异类约束解的迭代算法.利用修正共轭梯度法,求得了特殊双变量线性矩阵方程组的异类约束解,选取特殊的初始矩阵,得到唯一极小范数异类约束解.理论证明和数值算例验证了该方法的有限步收敛性,推广了修正共轭梯度法在求约束矩阵方程问题中的应用范围.This paper studies the method of finding different constrained solutions in the problem of constrained matrix equations.By modified conjugate gradient method and Choosing special initial matrix,different constrained solutions of special double-variable linear matrix equations is obtained,and the unique least-norm solution of the system is got.Theoretical proof and numerical examples show the finite-step convergence of the method,which extend the application of modified conjugate gradient method in solving constrained matrix equations.

关 键 词：线性矩阵方程组 异类约束解 修正共轭梯度法 最佳逼近 

分 类 号：O241.6[理学—计算数学]