求解矩阵方程AX=B的多步迭代算法  

Multi-step iterative algorithm for solving matrix equation AX=B

作　　者：周昱洁 彭振赟[1] 尚邵阳 ZHOU Yujie;PENG Zhenyun;SHANG Shaoyang(School of Mathematics and Computational Science,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《桂林电子科技大学学报》2020年第3期224-228,共5页Journal of Guilin University of Electronic Technology

基　　金：国家自然科学基金(61627807);广西自然科学基金(2017GXNSFAA198248,2018GXNSFBA281192);桂林电子科技大学研究生教育创新计划(2019YCXS084)。

摘　　要：为求解矩阵方程AX=B的一般解及其最小二乘问题,提出了一种多步迭代算法,给出并证明了由该算法产生的矩阵序列收敛于矩阵方程AX=B及其最小二乘问题的一般解和最小Frobenius范数解的条件。通过理论分析和数值实验证明了该算法的收敛性和有效性;数值结果表明,该算法的收敛速度比基于梯度的迭代算法更快。In order to solve the general solution of matrix equation AX=B and its least squares problem,a multi-step iterative algorithm is proposed.The conditions that the matrix sequence generated by the multi-step iterative algorithm converges to the general solution of the matrix equation AX=B and the minimum Frobenius norm solution of its least squares problem are given and proved;The convergence and effectiveness of the algorithm are proved by theoretical analysis and numerical experiments.Numerical results show that the multi-step iterative algorithm has a faster convergence speed than the gradient-based iterative algorithm proposed.

关 键 词：矩阵方程 最小二乘问题 基于梯度的迭代算法 不动点迭代法 多步迭代法 

分 类 号：O241.2[理学—计算数学]