同济大学学报（自然科学版）2024，Vol.52Issue(8)：1305-1311,7.DOI:10.11908/j.issn.0253-374x.22457
基于Count Sketch的预处理贪婪Kaczmarz方法
Preconditioning Greedy Kaczmarz Method Based on Count Sketch
摘要
Abstract
The convergence rate of greedy Kaczmarz method can be improved by introducing right preconditioner through orthogonal triangularization of coefficient matrix.However,when the number of rows of the coefficient matrix is much larger than the number of columns,the cost of orthogonal triangularization is too high.By introducing Count Sketch transform,a preconditioning greedy Kaczmarz method based on Count Sketch is proposed to reduce the cost.Convergence analysis of the new algorithm is provided,and the theoretical analysis shows that the new method has better convergence rate than the existing method when the condition number of coefficient matrix is large.The numerical experiments verified the effectiveness.关键词
Kaczmarz方法/预处理/Count Sketch/收敛性Key words
Kaczmarz method/preconditioning/Count Sketch/convergence property分类
数理科学引用本文复制引用
叶雨欣,殷俊锋..基于Count Sketch的预处理贪婪Kaczmarz方法[J].同济大学学报（自然科学版）,2024,52(8):1305-1311,7.基金项目
国家自然科学基金(11971354) （11971354）
