A Greedy Two-Subspace Randomized Kaczmarz Method for Solving Large Sparse Linear Systems

Abstract:

Based on an effective greedy probability criterion for selecting two working rows from a coefficient matrix， a greedy two-subspace randomized Kaczmarz method for solving large sparse linear systems is proposed. The theoretical analysis shows that this method converges to the minimal-norm solution of consistent linear systems， and the convergence factor of the method is smaller than that of the original two-subspace randomized Kaczmarz method. The numerical experiments show that this method is superior to the original two-subspace randomized Kaczmarz method from the point of view of solution performance.