矩阵方程AXB+CX^TD=F自反最小二乘解的迭代算法  

AN ITERATIVE METHOD FOR THE LEAST SQUARES REFLEXIVE MATRIX SOLUTION OF MATRIX EQUATION AXB+CX^TD=F

作　　者：袁飞[1] 张凯院[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》2009年第3期195-201,共7页Journal on Numerical Methods and Computer Applications

基　　金：陕西省自然科学基金资助项目(2006A05)

摘　　要：建立了求矩阵方程AXB+CX^TD=F的自反最小二乘解的迭代算法,证明了迭代算法的收敛性,该算法能够在有限步迭代计算之后得到矩阵方程的一个自反最小二乘解,或者极小范数自反最小二乘解。另外,还给出了在解集合中对给定矩阵的最佳逼近。An iterative method is presented to find the least squares reflexive matrix solution of the matrix equation AXB＋CX^TD = F.The convergence of the iterative method is proved.By this iterative method,its least squares reflexive matrix solution or least-norm least squares reflexive matrix solution can be got within finite steps.In addition,its optimal approximation solution to a given matrix in a given reflexive matrix solution set can be obtained.

关 键 词：矩阵方程 自反矩阵 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] O151.21[理学—数学]