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...

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Vydáno v:Numerical algorithms Ročník 99; číslo 1; s. 133 - 163
Hlavní autoři: He, Songnian, Wang, Ziting, Dong, Qiao-Li
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.05.2025
Springer Nature B.V
Témata:
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
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Popis
Shrnutí: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.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-024-01872-2