求解 ℳ张量多线性系统的一种新预处理Richardson迭代法
A New Preconditioned Richardson Iterative Method for Solving Multi-Linear Systems with ℳ-Tensors
摘要: Richardson迭代法是求解 ℳ 张量多线性系统的一种有效方法。为了进一步加快其收敛速度，本文给出一个新的预处理子并提出一种新预处理Richardson迭代法。理论上证明所提预处理Richardson迭代法的收敛性。最后，通过数值例子验证该方法的有效性和可行性。
Abstract: The Richardson iterative method is an effective method for solving multi-linear systems with ℳ -tensors. In this paper, a new preconditioner and new preconditioned Richardson iterative method are proposed to accelerate the convergence of multi-linear systems with ℳ -tensors. In the theory, the convergence of the preconditioned Richardson iterative method is proved. Finally, a numerical example is given to verify the effectiveness and feasibility of the proposed method.
文章引用：苟小飞. 求解 ℳ张量多线性系统的一种新预处理Richardson迭代法[J]. 应用数学进展, 2024, 13(11): 4753-4760. https://doi.org/10.12677/aam.2024.1311457

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