Randomized Kaczmarz iteration methods: Algorithmic extensions and convergence theory

We review and compare several representative and effective randomized projection iteration methods, including the randomized Kaczmarz method, the randomized coordinate descent method, and their modifications and extensions, for solving the large, sparse, consistent or inconsistent systems of linear...

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Bibliographic Details
Published in:Japan journal of industrial and applied mathematics Vol. 40; no. 3; pp. 1421 - 1443
Main Authors: Bai, Zhong-Zhi, Wu, Wen-Ting
Format: Journal Article
Language:English
Published: Tokyo Springer Japan 01.09.2023
Springer Nature B.V
Subjects:
Applications of Mathematics
Asymptotic methods
Computational Mathematics and Numerical Analysis
Convergence
Eigenvalues
Iterative methods
Linear equations
Mathematics
Mathematics and Statistics
Methods
Survey
Theorems
System of linear equations
Randomized projection iteration
65K05
65F10
90C25
Coordinate descent method
Convergence property
Kaczmarz method
65F20
15A06
CR: G1.3
ISSN:0916-7005, 1868-937X
Online Access:Get full text
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Summary:We review and compare several representative and effective randomized projection iteration methods, including the randomized Kaczmarz method, the randomized coordinate descent method, and their modifications and extensions, for solving the large, sparse, consistent or inconsistent systems of linear equations. We also anatomize, extract, and purify the asymptotic convergence theories of these iteration methods, and discuss, analyze, and summarize their advantages and disadvantages from the viewpoints of both theory and computations.
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ISSN:0916-7005
1868-937X
DOI:10.1007/s13160-023-00586-7