实矩阵两类广义逆的迭代算法  

ITERATIVE ALGORITHM FOR MOORE-PENROSE INVERSE AND DRAZIN INVERSE OF REAL MATRIX

作　　者：张凯院[1] 宁倩芝 

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》2015年第2期81-90,共10页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(11071196)

摘　　要：将计算实矩阵的Moore-Penrose逆和Drazin逆转化为线性矩阵方程组的求解问题,然后采用修正共轭梯度法求线性矩阵方程组的一般解,并通过简单的矩阵乘法运算或者直接得到实矩阵的Moore-Penrose逆和Drazin逆.修正共轭梯度法不同于通常的共轭梯度法,它不要求涉及的线性代数方程组的系数矩阵正定、可逆或者列满秩,因此总是可行的.数值算例表明,这种算法是有效的.The computation of the Moore-Penrose inverse and Drazin inverse of real matrix can be transformed into solving the problem of linear matrix equations. Then the modified conjugate gradient method can be used to get the general solution of linear matrix equations. Finally, the Moore-Penrose inverse and Drazin inverse of real matrix can be obtained directly or through matrix multiplication.. The modified conjugate gradient method is different from the usual conjugate gradient method. It which does not require the positive definite, reversible or full column rank of the coefficient matrix of the involved linear algebraic equations. Thus this method is always feasible. The numerical experiments show that the algorithm is effective.

关 键 词：Moore—Penrose逆 DRAZIN逆 线性矩阵方程组 修正共轭梯度法 迭代算法 

分 类 号：O151.21[理学—数学]