Restarted randomized surrounding methods for solving large linear equations

TL;DR

This paper introduces restarted randomized surrounding methods that enhance the efficiency of solving large linear equations, with proven convergence and superior performance demonstrated through numerical experiments in various applications.

Contribution

The paper proposes a novel class of restarted randomized surrounding algorithms with theoretical convergence analysis and improved practical performance over existing methods.

Findings

Convergence is proven under randomized row selection.

The methods outperform existing algorithms in numerical experiments.

Effective in over-determined, under-determined systems, and image processing applications.

Abstract

A class of restarted randomized surrounding methods are presented to accelerate the surrounding algorithms by restarted techniques for solving the linear equations. Theoretical analysis prove that the proposed method converges under the randomized row selection rule and the expectation convergence rate is also addressed. Numerical experiments further demonstrate that the proposed algorithms are efficient and outperform the existing method for over-determined and under-determined linear equation, as well as in the application of image processing.