论求解大型不一致线性系统的多步扩展最大残差 Kaczmarz 法

IF 1.1 3区数学 Q1 MATHEMATICS

Results in Mathematics Pub Date : 2024-06-14 DOI:10.1007/s00025-024-02210-7

A.-Qin Xiao, Jun-Feng Yin, Ning Zheng

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引用次数: 0

摘要

本文提出了一种多步扩展最大残差 Kaczmarz 法，利用多步迭代技术求解大型不一致线性方程组。理论分析证明了所提出的方法是收敛的，并给出了其收敛速率的上限。数值实验表明，所提出的方法是有效的，在迭代步数和计算成本方面优于现有的扩展 Kaczmarz 方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

On Multi-step Extended Maximum Residual Kaczmarz Method for Solving Large Inconsistent Linear Systems

查看原文本刊更多论文

On Multi-step Extended Maximum Residual Kaczmarz Method for Solving Large Inconsistent Linear Systems

A multi-step extended maximum residual Kaczmarz method is presented for the solution of the large inconsistent linear system of equations by using the multi-step iterations technique. Theoretical analysis proves the proposed method is convergent and gives an upper bound on its convergence rate. Numerical experiments show that the proposed method is effective and outperforms the existing extended Kaczmarz methods in terms of the number of iteration steps and the computational costs.

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来源期刊

Results in Mathematics 数学-数学

CiteScore

1.90

自引率

4.50%

发文量

198

审稿时长

6-12 weeks

期刊介绍： Results in Mathematics (RM) publishes mainly research papers in all fields of pure and applied mathematics. In addition, it publishes summaries of any mathematical field and surveys of any mathematical subject provided they are designed to advance some recent mathematical development.