Restarted randomized surrounding methods for solving large linear equations

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 shows that the proposed method converges under the randomized row selection rule and the convergence rate in expectation is also addressed. Numerical experiments further demonstrate that the proposed algorithms are efficient and outperform the existing method for overdetermined and underdetermined linear equations, as well as in the application of image processing.