| Volume 15, Number 2, 2025, Pages - DOI：10.11948/JAAC-2024-0208 |
| On weighted average fast block Kaczmarz methods for solving large consistent linear systems |
| Hong-Yu Li,Xin-Hui Shao |
| Keywords:Consistent systems, Greedy distance, Weighted average, Block Kaczmarz method |
| Abstract: |
| To solve large consistent linear systems, a weighted average fast block Kaczmarz(WAFBK)
method is proposed, which is based on the ideas of greedy distance and weighted average. This
method does not require the calculation of pseudoinverses of submatrices. Furthermore, we
provide a detailed analysis of the convergence properties of various methods, corresponding to
four different weights used in the selection probability criterion. And it has been proven that
WAFBK-type methods converge to the unique least-norm solutions of linear systems. Numerical
results conffrm the effectiveness of the WAFBK-type methods and demonstrate their ability to
accelerate the convergence rate of the fast deterministic block Kaczmarz method. |
PDF Download reader
|
|
|
|