Multi-step greedy Kaczmarz algorithms with simple random sampling for solving large linear systems

被引：4

作者：

Zhang, Ke ^{[1
]}

Li, Fu-Ting ^{[1
]}

Jiang, Xiang-Long ^{[1
]}

机构：

[1] Shanghai Maritime Univ, Dept Math, Shanghai 201306, Peoples R China

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2022年 / 41卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Linear systems; Kaczmarz method; Randomized Kaczmarz method; Greedy randomized Kaczmarz method; Simple random sampling; BLOCK KACZMARZ;

D O I：

10.1007/s40314-022-02044-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

By exploiting the simple random sampling and the greedy technique for capturing large residual entries, we put forth two multi-step greedy Kaczmarz algorithms for solving large linear systems. Both algorithms employ simple random sampling ab initio yet differ in the rules for choosing the working row. The new algorithms are proved to be convergent when the linear system is consistent. Some numerical experiments are carried out to verify the effectiveness of the proposed algorithms.

引用

页数：25

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