求逆矩阵的2种新算法  

Two new algorithms for computing inverse matrix

作　　者：刘东甲[1] LIU Dongjia(School of Resources and Environmental Engineering,Hefei University of Technology,Hefei 230009,Chin)

机构地区：[1]合肥工业大学资源与环境工程学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2018年第5期714-720,共7页Journal of Hefei University of Technology：Natural Science

基　　金：安徽省国土资源厅科研资助项目(2010-g-32)

摘　　要：基于无穷限广义积分表示的逆矩阵公式,文章在积分区间[0,+∞)上给定公比为q(q为大于1的整数)的等比数列,再分别由矩阵指数及其积分在该数列上的值构造2个矩阵序列,据此给出求逆矩阵的2种算法;证明了这2种算法均具有q阶收敛速度。算法1要求相应的非奇异矩阵满足一定的条件;算法2适用于各类非奇异矩阵。算例表明,这2种算法具有高稳定性和高精度。Based on the inverse matrix formula of the infinite generalized integral,ageometric sequence is given in the integral interval[0,＋∞）,whose common ratioqis an integer greater than one,and two matrix sequences are constructed by the matrix index and the value of its integral at the sequence.On this basis,the recursive algorithm and the iterative algorithm of the inverse matrix are given,and it is proved that both algorithms have q-order convergence rate.The recursive algorithm is required to satisfy certain condition of the nonsingular matrix,and the iterative algorithm is applicable to all types of nonsingular matrices.Numerical examples show that these two algorithms have high stability and accuracy.

关 键 词：逆矩阵公式 矩阵序列 递推公式 算法 

分 类 号：O151.21[理学—数学]