并行迭代混合Gauss-Jacobi-Seidel方法

IF 2.1 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-03-22 DOI:10.1016/j.cam.2025.116629

Matheus da Silva Menezes , Paulo Henrique Lopes Silva , João Paulo Caraú de Oliveira , Raimundo Leandro Andrade Marques , Ivan Mezzomo

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引用次数: 0

摘要

本文在Gauss-Jacobi和Gauss-Seidel方法的基础上，提出了求解线性代数系统的一种新的迭代混合方法，称为Jacobi-Seidel并行迭代法，简称JASPIoM。该方法显示了一个允许并行处理的迭代矩阵，可以在串行或并行体系结构中使用。给出了该方法的数学公式，并在并行环境下进行了测试，并考虑执行时间，与串行和并行化高斯-雅可比法和串行高斯-塞德尔法进行了比较。计算实验的目的是关注性能的差异，考虑在串行和并行环境下的执行加速。结果表明，JASPIoM方法具有良好的性能，表明了该方案的有效性和潜力。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A Parallel Iterative hybrid Gauss–Jacobi–Seidel method

In this paper, we introduce a new iterative hybrid method to find the solution of linear algebraic systems based on the Gauss–Jacobi and Gauss–Seidel methods, named Jacobi–Seidel Parallel Iterative Method, JASPIoM for short. This method shows a iteration matrix that allows to parallelize the processing and can be utilized in serial or parallel architectures. The mathematical formulation is presented and the tests are performed in parallel ambiance and its performance is evaluated, considering the time of execution, in comparison to the serial and parallelized Gauss–Jacobi method and serial Gauss–Seidel method. The computational experiment aimed at focusing on the differences in performance, considering the speedup of execution in serial and parallel context. The results show that the JASPIoM method presents good performance, indicating the efficiency and potential of this scheme.

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.