On Greedy Two-subspace Extended Kaczmarz Method for Solving Coherent Linear Least-squares Problems

Abstract:

Based on an effective sampling strategy named the maximum distance rule， a greedy two-subspace extended Kaczmarz method is proposed for solving coherent linear least-squares problems. Theoretical analysis gives the convergence rate of the greedy two-subspace extended Kaczmarz method and the tighter upper bound of the convergence rate of the two-subspace randomized extended Kaczmarz method. Numerical experiments show that the greedy two-subspace extended Kaczmarz method outperforms the two-subspace randomized extended Kaczmarz method and the random double block Kaczmarz method in terms of the number of iteration steps and CPU time.