Inertial randomized Kaczmarz algorithms for solving coherent linear systems

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Numerical Algorithms Pub Date : 2024-07-05 DOI:10.1007/s11075-024-01872-2

Songnian He, Ziting Wang, Qiao-Li Dong

引用次数: 0

Abstract

In this paper, by regarding the two-subspace Kaczmarz method as an alternated inertial randomized Kaczmarz algorithm we present a better convergence rate estimate under a mild condition. Furthermore, we accelerate the alternated inertial randomized Kaczmarz algorithm and introduce a multi-step inertial randomized Kaczmarz algorithm which is proved to have a faster convergence rate. Numerical experiments support the theory results and illustrate that the multi-inertial randomized Kaczmarz algorithm significantly outperform the two-subspace Kaczmarz method in solving coherent linear systems.

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求解相干线性系统的惯性随机卡兹马兹算法

在本文中，我们将双子空间 Kaczmarz 方法视为交替惯性随机 Kaczmarz 算法，在温和条件下提出了更好的收敛率估计。此外，我们加速了交替惯性随机化 Kaczmarz 算法，并引入了一种多步惯性随机化 Kaczmarz 算法，该算法被证明具有更快的收敛速度。数值实验支持了理论结果，并说明多惯性随机 Kaczmarz 算法在求解相干线性系统时明显优于双子空间 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。

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来源期刊

Numerical Algorithms 数学-应用数学

CiteScore

4.00

自引率

9.50%

发文量

201

审稿时长

9 months

期刊介绍： The journal Numerical Algorithms is devoted to numerical algorithms. It publishes original and review papers on all the aspects of numerical algorithms: new algorithms, theoretical results, implementation, numerical stability, complexity, parallel computing, subroutines, and applications. Papers on computer algebra related to obtaining numerical results will also be considered. It is intended to publish only high quality papers containing material not published elsewhere.