Randomized block subsampling Kaczmarz-Motzkin method

TL;DR

This paper introduces a novel randomized block Kaczmarz-Motzkin method that combines randomness and greed to efficiently solve linear systems, with proven linear convergence and verified numerical performance.

Contribution

It proposes a new subsampling strategy that extends existing methods by integrating randomness and greed, improving convergence and efficiency.

Findings

Method converges linearly in expectation

Numerical examples confirm efficiency and feasibility

Combines advantages of randomness and greed strategies

Abstract

By introducing a subsampling strategy, we propose a randomized block Kaczmarz-Motzkin method for solving linear systems. Such strategy not only determines the block size, but also combines and extends two famous strategies, i.e., randomness and greed, and hence can inherit their advantages. Theoretical analysis shows that the proposed method converges linearly in expectation to the least-Euclidean-norm solution. Several numerical examples are reported to verify the efficiency and feasibility of the new method.