Parameterized Randomized Kaczmarz Method for Solving Large Sparse Linear Systems

Abstract

In order to solve large sparse linear systems, we introduce a relaxation factor into the iterative formula based on the randomized Kaczmarz method. According to this idea, a parameterized randomized Kaczmarz method is constructed. Then, the convergence of this method is proved when the linear systems are consistent. Numerical experiments show that this method has better performance than the randomized Kaczmarz method when the appropriate relaxation factor is selected, mainly in less computing time and the number of the iteration steps.