In this paper, we present a respectively scaled splitting (RSS) iteration method for the block 4-by-4 linear system from eddy current electromagnetic problems. Unconditional convergence properties of the RSS iteration method are established. Theoretical results show that the quasi-optimal iterative parameter that minimizes the spectral radius is $$\alpha _{opt}=1$$ and the corresponding convergence factor is no more than $$\frac{1}{2}$$ . The validity of theoretical analysis and the effectiveness of RSS methods are verified by numerical experiments.

中文翻译：

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涡流电磁问题中一类分块4×4线性系统的分别标度分裂迭代法

在本文中，我们针对涡流电磁问题中的块 4×4 线性系统提出了一种分别缩放的分裂 (RSS) 迭代方法。建立了RSS迭代方法的无条件收敛特性。理论结果表明，最小化谱半径的准最优迭代参数为$$\alpha _{opt}=1$$，对应的收敛因子不超过$$\frac{1}{2}$$。数值实验验证了理论分析的有效性和RSS方法的有效性。