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Keywords = randomized block Kaczmarz

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15 pages, 491 KiB  
Article
Randomized Block Kaczmarz Methods for Inner Inverses of a Matrix
by Lili Xing, Wendi Bao, Ying Lv, Zhiwei Guo and Weiguo Li
Mathematics 2024, 12(3), 475; https://doi.org/10.3390/math12030475 - 2 Feb 2024
Viewed by 1363
Abstract
In this paper, two randomized block Kaczmarz methods to compute inner inverses of any rectangular matrix A are presented. These are iterative methods without matrix multiplications and their convergence is proved. The numerical results show that the proposed methods are more efficient than [...] Read more.
In this paper, two randomized block Kaczmarz methods to compute inner inverses of any rectangular matrix A are presented. These are iterative methods without matrix multiplications and their convergence is proved. The numerical results show that the proposed methods are more efficient than iterative methods involving matrix multiplications for the high-dimensional matrix. Full article
(This article belongs to the Section E: Applied Mathematics)
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15 pages, 321 KiB  
Article
On the Convergence of the Randomized Block Kaczmarz Algorithm for Solving a Matrix Equation
by Lili Xing, Wendi Bao and Weiguo Li
Mathematics 2023, 11(21), 4554; https://doi.org/10.3390/math11214554 - 5 Nov 2023
Cited by 2 | Viewed by 1801
Abstract
A randomized block Kaczmarz method and a randomized extended block Kaczmarz method are proposed for solving the matrix equation AXB=C, where the matrices A and B may be full-rank or rank-deficient. These methods are iterative methods without matrix [...] Read more.
A randomized block Kaczmarz method and a randomized extended block Kaczmarz method are proposed for solving the matrix equation AXB=C, where the matrices A and B may be full-rank or rank-deficient. These methods are iterative methods without matrix multiplication, and are especially suitable for solving large-scale matrix equations. It is theoretically proved that these methods converge to the solution or least-square solution of the matrix equation. The numerical results show that these methods are more efficient than the existing algorithms for high-dimensional matrix equations. Full article
(This article belongs to the Section E: Applied Mathematics)
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