关于求解矩阵方程AXB = C的广义Richardson迭代及其收敛性  

The Generalized Richardson Iteration for Solving the Matrix Equation AXB = C and Its Convergence Analysis

作　　者：何依琳 

机构地区：[1]长沙理工大学数学与统计学院,湖南 长沙

出　　处：《应用数学进展》2024年第7期3257-3265,共9页Advances in Applied Mathematics

摘　　要：本文研究了对于方程AXB = C在传统的Richardson方法基础上,与外推法结合得到的广义Richardson迭代方法。首先,提出广义Richardson迭代方法,然后证明其收敛性。最后,通过数值实验,验证了该迭代方法比传统的渐进迭代逼近法方法(PIA)更有效。This paper investigates the generalized Richardson iterative method for solving the matrix equation AXB = C, which combines extrapolation with the traditional Richardson method. Initially, the generalized Richardson iterative method is proposed, followed by the proof of its convergence. Finally, through numerical experiments, it is verified that this iterative method is more effective than the traditional Progressive Iterative Approximation (PIA) approach.

关 键 词：渐进迭代逼近矩阵方程 曲面拟合 外推法 广义Richarson 

分 类 号：O15[理学—数学]