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Article overview
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On the alternating randomized block Kaczmarz method | | Nian-Ci Wu
; Yang Zhou
; Zhaolu Tian
; | | Date: |
1 Nov 2023 | | Abstract: | The block Kaczmarz method and its variants are designed for solving the
over-determined linear system. They involve iteratively projecting the current
point onto the solution space of a subset of constraints. In this work, by
alternately dealing with two subproblems (i.e., linear system with multiple
right-hand sides) using the block Kaczmarz method, we propose the {it
Alternating Randomized Block Kaczmarz} (ARBK) method to solve the linear matrix
equation $AXB=F$, which incorporates a randomized index selection scheme to
determine the subset of constraints. The convergence analysis reveals that the
ARBK method has a linear convergence rate bounded by an explicit expression.
Several numerical studies have been conducted to validate the theoretical
findings. | | Source: | arXiv, 2311.00199 | | Services: | Forum | Review | PDF | Favorites | |
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