On Relaxed Greedy Randomized Augmented Kaczmarz Methods for Solving Large Sparse Inconsistent Linear Systems

Abstract

For solving large-scale sparse inconsistent linear systems by iteration methods, we introduce a relaxation parameter in the probability criterion of the greedy randomized augmented Kaczmarz method, obtaining a class of relaxed greedy randomized augmented Kaczmarz methods. We prove the convergence of these methods and estimate upper bounds for their convergence rates. Theoretical analysis and numerical experiments show that these methods can perform better than the greedy randomized augmented Kaczmarz method if the relaxation parameter is chosen appropriately.