A class of residual-based extended Kaczmarz methods for solving inconsistent linear systems

Bao, Wendi; Lv, Zhonglu; Zhang, Feiyu; Li, Weiguo

doi:10.1016/j.cam.2022.114529

Cited by 7 publications

(2 citation statements)

References 13 publications

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“…It is unfavorable when the size of A is large. For more variants and studies of row-action iterative methods, we refer to [4,5,13,17,28,30,33] and the references therein.…”

Section: The Randomized Multiple Row-action Methodsmentioning

confidence: 99%

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

Wu,

Liu,

Wang

et al. 2024

Preprint

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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. AMS subject classifications: 65F10, 65F20, 65F25, 65D10, 68W20

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“…It is unfavorable when the size of A is large. For more variants and studies of row-action iterative methods, we refer to [4,5,13,17,28,30,33] and the references therein.…”

Section: The Randomized Multiple Row-action Methodsmentioning

confidence: 99%

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

Wu,

Liu,

Wang

et al. 2024

Preprint

View full text Add to dashboard Cite

show abstract

“…It is unfavorable when the size of A is large. For more variants and studies of row iterative methods, we refer to [4,5,11,14,25,27,30] and the references therein.…”

Section: Preparationmentioning

confidence: 99%

On two-subspace randomized extended Kaczmarz method for solving large linear least-squares problems

2021

Numer Algor

View full text Add to dashboard Cite

The randomized row 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 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.

show abstract

A residual-based surrogate hyperplane extended Kaczmarz algorithm for large least squares problems

Zhang,

Chen,

Jiang

2024

Calcolo

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A class of residual-based extended Kaczmarz methods for solving inconsistent linear systems

Cited by 7 publications

References 13 publications

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

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

On two-subspace randomized extended Kaczmarz method for solving large linear least-squares problems

A residual-based surrogate hyperplane extended Kaczmarz algorithm for large least squares problems

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