%0 Journal Article
%T 关于求解矩阵方程<i>AXB </i>= <i>C</i>的广义Richardson迭代及其收敛性<br>The Generalized Richardson Iteration for Solving the Matrix Equation <i>AXB</i> = <i>C</i> and Its Convergence Analysis
%A 何依琳
%J Advances in Applied Mathematics
%P 3257-3265
%@ 2324-8009
%D 2024
%I Hans Publishing
%R 10.12677/aam.2024.137312
%X 本文研究了对于方程<i>AXB</i> = <i>C</i>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。<br />
This paper investigates the generalized Richardson iterative method for solving the matrix equation <i>AXB</i> = <i>C</i>, 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.
%K 渐进迭代逼近矩阵方程，曲面拟合，外推法，广义Richarson<br>Progressive Iterative Approximation Method
%K Surface Fitting
%K Extrapolation Method
%K Generalized Richarson
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=91774