Article
Version 1
Preserved in Portico This version is not peer-reviewed
On the Convergence of Randomized Block Kaczmarz Algorithm for Solving Matrix Equation
Version 1
: Received: 10 October 2023 / Approved: 11 October 2023 / Online: 11 October 2023 (07:42:21 CEST)
A peer-reviewed article of this Preprint also exists.
Xing, L.; Bao, W.; Li, W. On the Convergence of the Randomized Block Kaczmarz Algorithm for Solving a Matrix Equation. Mathematics 2023, 11, 4554. Xing, L.; Bao, W.; Li, W. On the Convergence of the Randomized Block Kaczmarz Algorithm for Solving a Matrix Equation. Mathematics 2023, 11, 4554.
Abstract
Randomized block Kaczmarz Method and randomized extended block Kaczmarz Method are proposed for solving matrix equation AXB=C, where the matrix 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 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.
Keywords
matrix equation; randomized block Kaczmarz; randomized extended block Kaczmarz; convergence
Subject
Computer Science and Mathematics, Computational Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment