Inertial randomized Kaczmarz algorithms for solving coherent linear systems

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 inert...

Full description

Saved in:
Bibliographic Details
Published in:Numerical algorithms Vol. 99; no. 1; pp. 133 - 163
Main Authors: He, Songnian, Wang, Ziting, Dong, Qiao-Li
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2025
Springer Nature B.V
Subjects:
Algebra
Algorithms
Computer Science
Convergence
Convex analysis
Eigenvalues
Linear equations
Linear systems
Methods
Numeric Computing
Numerical Analysis
Original Paper
Random variables
Subspaces
Theory of Computation
System of linear equations
Two-subspace Kaczmarz method
Inertial randomized Kaczmarz algorithm
Randomized Kaczmarz algorithm
65J20
47J06
Inertial extrapolation
ISSN:1017-1398, 1572-9265
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-024-01872-2