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

作　　者：苟小飞 

机构地区：[1]西北师范大学数学与统计学院,甘肃 兰州

出　　处：《应用数学进展》2024年第11期4753-4760,共8页Advances in Applied Mathematics

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。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.

关 键 词：多线性系统 张量 Richardson迭代法 预处理子 收敛性 

分 类 号：O24[理学—计算数学]