A greedy average block Kaczmarz method for the large scaled consistent system of linear equations

被引：5

作者：

Wen, Li ^{[1
,2
]}

Yin, Feng ^{[1
,2
]}

Liao, Yimou ^{[1
]}

Huang, Guangxin ^{[3
]}

机构：

[1] Sichuan Univ Sci & Engn, Coll Math & Stat, Zigong 643000, Peoples R China

[2] Sichuan Univ Sci & Engn, Sichuan Prov Univ Key Lab Bridge Nondestruct Dete, Zigong 643000, Peoples R China

[3] Chengdu Univ Technol, Coll Math & Phys, Geomath Key Lab Sichuan, Chengdu 610059, Peoples R China

来源：

AIMS MATHEMATICS | 2022年 / 7卷 / 04期

关键词：

block Kaczmarz; extrapolated stepsize; greedy strategy; GABK; ITERATIVE ALGORITHMS;

D O I：

10.3934/math.2022378

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents a greedy average block Kaczmarz (GABK) method to solve the large scaled consistent system of linear equations. The GABK method introduces the strategy of extrapolation process to improve the GBK algorithm and to avoid computing the Moore-Penrose inverse of a submatrix of the coefficient matrix determined by the block index set. The GABK method is proved to converge linearly to the least-norm solution of the consistent system of linear equations. Numerical examples show that the GABK method has the best efficiency and effectiveness among all methods compared.

引用

页码：6792 / 6806

页数：15

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