多变量矩阵方程组一种异类约束解的迭代算法  

AN ITERATIVE ALGORITHM FOR SOLVING A MULTI-VARIABLES MATRIX EQUATIONS OVER DIFFERENT CONSTRAINED MATRICES

作　　者：武见[1] 张凯院[1] 刘晓敏[1] 

机构地区：[1]西北工业大学应用数学系,西安710072

出　　处：《数值计算与计算机应用》2011年第2期105-116,共12页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11071196)

摘　　要：借鉴求线性矩阵方程组同类约束解的修正共轭梯度法,建立了求多个未知矩阵的线性矩阵方程组的一种异类约束解的修正共轭梯度法,并证明了该算法的收敛性.利用该算法不仅可以判断矩阵方程组的异类约束解是否存在,而且在有异类约束解,且不考虑舍入误差时,可在有限步计算后求得矩阵方程组的一组异类约束解;选取特殊初始矩阵时,可求得矩阵方程组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组异类约束解集合中的最佳逼近.算例表明,该算法是有效的.On the base of the modified conjugate gradient for solving the same constramea solution of the linear matrix equations, a modified conjugate method is presented for solving a linear matrix equations with several unknown matrices over different constrained matrices. The convergence of this method is also given. By this method, we not only can judge whether the matrix equations is consistent over different constrained matrices, but also can obtain the solution within finite iterative steps in the absence of round off errors when the matrix equations is consistent, and the different constrained solution with least-norm can be got by choosing special initial matrices. In addition, the optimal approximation matrix of the given matrix can be obtained in the set of the different constrained solution. The numerical example show that the method is quite efficient.

关 键 词：线性矩阵方程组 异类约束矩阵 修正共轭梯度法 收敛性 最佳逼近 

分 类 号：O241.6[理学—计算数学]