关于连续性Sylvester方程的广义Richardson迭代
On the Generalized Richardson Iteration of the Continuous Sylvester Equation
摘要: 本文研究当系数矩阵A和B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。
Abstract: In this paper, we study the generalized Richardson iteration for solving the continuous Sylvester equationAX+XB=C, where the coefficient matrices A and B 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 ω, and emphasize the effectiveness of the proposed method by comparing it with the HSS method.
文章引用：蒋兰. 关于连续性Sylvester方程的广义Richardson迭代[J]. 应用数学进展, 2024, 13(7): 3241-3249. https://doi.org/10.12677/aam.2024.137310

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