On the randomized multiple row-action methods for solving linear least-squares problems

The randomized row-action method is a popular representative of the iterative algorithm because of its efficiency in solving the overdetermined and consistent systems of linear equations. In this paper, we present an extended randomized multiple row-action method to solve a given overdetermined and...

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Bibliographic Details
Published in:Numerical algorithms Vol. 100; no. 3; pp. 893 - 920
Main Authors: Zuo, Qian, Wu, Nian-Ci, Liu, Chengzhi, Wang, Yatian
Format: Journal Article
Language:English
Published: New York Springer US 01.11.2025
Springer Nature B.V
Subjects:
Algebra
Algorithms
Approximation
CAD
Computer aided design
Computer Science
Image reconstruction
Iterative algorithms
Least squares method
Linear equations
Linear systems
Methods
Numeric Computing
Numerical Analysis
Theory of Computation
68W20
65F10
65D10
65F20
65F25
Real-world application
Randomized algorithm
Row-action method
Convergence analysis
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:The randomized row-action method is a popular representative of the iterative algorithm because of its efficiency in solving the overdetermined and consistent systems of linear equations. In this paper, we present an extended randomized multiple row-action method to solve a given overdetermined and inconsistent linear system and analyze its computational complexities at each iteration. We prove that the proposed method can linearly converge in the mean square to the least-squares solution with a minimum Euclidean norm. Several numerical studies are presented to corroborate our theoretical findings. The real-world applications, such as image reconstruction and large noisy data fitting in computer-aided geometric design, are also presented for illustration purposes.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-024-01972-z