线性和非线性系统迭代解算器的快速参数优化框架

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-07-09 DOI:10.1016/j.aml.2025.109660

Wei Li , Wenlong Wang , Pingfei Dai , Qingbiao Wu

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引用次数: 0

摘要

用矩阵分裂迭代法求解方程，必须确定最优参数，使迭代次数最少。本文采用基于贝叶斯优化的搜索范式来寻找线性和非线性迭代方法的最优参数，并提供了大量的数值实验来评估和对比该方法与传统区间遍历的搜索性能。数值结果表明，与线性和非线性系统矩阵分裂迭代方法中的区间遍历法相比，贝叶斯优化方法不仅迭代次数最少，而且效率更高。

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A fast parameter optimization framework for iterative solvers in linear and nonlinear systems

To solve the equation using the matrix-splitting iterative method, it is essential to determine the optimal parameters so as to minimize the number of iterations. In this paper, a search paradigm based on Bayesian optimization is used to find the optimal parameters of linear and nonlinear iterative methods, and a large number of numerical experiments are provided to assess and contrast the search performance of the method against that of the traditional interval traversal. The numerical results show that compared with interval traversal in the iterative methods of matrix splitting for linear and nonlinear systems, the optimal parameters searched by Bayesian optimization can not only have the least number of iterations but also be more efficient.

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.