%0 Journal Article
%T 关于连续性Sylvester方程的广义Richardson迭代<br>On the Generalized Richardson Iteration of the Continuous Sylvester Equation
%A 蒋兰
%J Advances in Applied Mathematics
%P 3241-3249
%@ 2324-8009
%D 2024
%I Hans Publishing
%R 10.12677/aam.2024.137310
%X 本文研究当系数矩阵<i>A</i>和<i>B</i>是正半定矩阵，且它们至少有一个是正定时求解连续Sylvester方程的迭代解AX+XB=C的广义Richardson迭代。我们首先分析了求解这类Sylvester方程的广义理查森迭代的收敛性，然后推导了它的最小谱半径的上界以及参数ω的最佳值，通过于HSS方法的比较，强调了所提方法的有效性。<br />
In this paper, we study the generalized Richardson iteration for solving the continuous Sylvester equationAX+XB=C, where the coefficient matrices <i>A</i> and <i>B </i>are assumed to be positive semidefinite and at least one of them is positive definite. We first analyze the convergence of the generalized Richardson iteration for solving such a class of Sylvester equations, then derive the upper bound of the minimum spectral radius and the best value of the parameter <i>ω</i>, and emphasize the effectiveness of the proposed method by comparing it with the HSS method.
%K 广义Richardson算法，Sylvester方程，松弛参数，谱半径<br>Generalized Richardson Iteration
%K Sylvester Equation
%K Relaxation Parameters
%K Spectral Radius
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=91772