Greedy Randomized-Distance Kaczmarz Method for Solving Large Sparse Linear Systems

Abstract:

Based on a new probability criterion to select the working rows from the coefficient matrix, a greedy-distance randomized Kaczmarz method was proposed to solve large sparse linear systems. The theoretical analysis demonstrates that this method converges to the least-norm solution when the linear system is consistent, and the convergence factor of the greedy-distance randomized Kaczmarz method is smaller than that of the randomized Kaczmarz method. Moreover, the numerical results have verified its effectiveness.

Key words:Kaczmarz method;sparse linear systems;convergence property;randomized iteration