求多变量矩阵方程异类约束解的迭代算法  

An Iterative Approaching to Different Constraints Solution of Multivariable Matrix Equation

作　　者：张凯院[1] 武见[1] 

机构地区：[1]西北工业大学理学院,陕西西安710072

出　　处：《中北大学学报（自然科学版）》2012年第3期232-239,共8页Journal of North University of China(Natural Science Edition)

基　　金：教育部新世纪优秀人才支持计划资助项目(NCET)

摘　　要：基于求线性矩阵方程同类约束解的修正共轭梯度法,建立了求多变量线性矩阵方程异类约束解的修正共轭梯度法,证明了该算法在有限步计算后可得到矩阵方程的一组异类约束解,当选取特殊初始矩阵时可得到矩阵方程的极小范数异类约束解.另外,还可求得指定矩阵在该矩阵方程异类约束解集合中的最佳逼近.Based on the modified conjugate gradient method that is used in finding the same constraint solution of the matrix equation,a modified conjugate method was proposed to find the different constraints solution of multivariable matrix equation.With this method,the different constraints solution can be obtained within finite iterative steps in the absence of round off errors.The different constraints solution with least-norm can be got if some special initial matrix is chosen.In addition,the optimal approximation matrix of a given matrix can be obtained in the set of the different constraints solution.

关 键 词：矩阵方程 异类约束矩阵 修正共轭梯度法 最佳逼近 极小范数解 

分 类 号：O241.6[理学—计算数学]