Finding solution of linear systems via new forms of BiCG, BiCGstab and CGS algorithms

IF 2.6 3区数学

Computational and Applied Mathematics Pub Date : 2024-08-07 DOI:10.1007/s40314-024-02867-4

Hojjatollah Shokri Kaveh, Masoud Hajarian, Anthony. T. Chronopoulos

引用次数: 0

Abstract

This paper introduces some Krylov subspace methods utilizing the s-step technique. The variable s-step technique is applied to CGS and BiCG algorithms, and extended to the BiCGstab algorithm as an intermediate state between this two algorithms. By proposing the use of the s parameter as a variable, these algorithms become adaptable. To enhance stability, a regularization technique is incorporated. Through the integration of these techniques, stable algorithms are developed. Numerical examples are provided to demonstrate the efficacy and quality of the proposed algorithms.

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通过新形式的 BiCG、BiCGstab 和 CGS 算法寻找线性系统的解决方案

本文介绍了一些利用 s 步技术的 Krylov 子空间方法。变量 s 步技术应用于 CGS 和 BiCG 算法，并扩展到 BiCGstab 算法，作为这两种算法之间的中间状态。通过提出使用 s 参数作为变量，这些算法变得具有适应性。为了提高稳定性，还加入了正则化技术。通过整合这些技术，开发出了稳定的算法。我们提供了数值示例来证明所提算法的功效和质量。

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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来源期刊

Computational and Applied Mathematics MATHEMATICS, APPLIED-

自引率

11.50%

发文量

352

期刊介绍： Computational & Applied Mathematics began to be published in 1981. This journal was conceived as the main scientific publication of SBMAC (Brazilian Society of Computational and Applied Mathematics). The objective of the journal is the publication of original research in Applied and Computational Mathematics, with interfaces in Physics, Engineering, Chemistry, Biology, Operations Research, Statistics, Social Sciences and Economy. The journal has the usual quality standards of scientific international journals and we aim high level of contributions in terms of originality, depth and relevance.