On fast greedy block Kaczmarz methods for solving large consistent linear systems

TL;DR

This paper introduces fast greedy block Kaczmarz methods that leverage greedy strategies and averaging techniques, demonstrating improved efficiency and convergence for large consistent linear systems through theoretical analysis and numerical experiments.

Contribution

It proposes novel fast greedy block Kaczmarz algorithms with convergence analysis and shows they outperform existing methods in efficiency.

Findings

Methods are theoretically convergent.

Numerical experiments confirm faster convergence.

Outperforms existing algorithms in efficiency.

Abstract

A class of fast greedy block Kaczmarz methods combined with general greedy strategy and average technique are proposed for solving large consistent linear systems. Theoretical analysis of the convergence of the proposed method is given in detail. Numerical experiments show that the proposed methods are efficient and faster than the existing methods.