On Greedy Randomized Kaczmarz Method for Solving Large Sparse Linear Systems

For solving large-scale systems of linear equations by iteration methods, we introduce an effective probability criterion for selecting the working rows from the coefficient matrix and construct a greedy randomized Kaczmarz method. It is proved that this method converges to the unique least-norm solution of the linear system when it is consistent. Theoretical analysis demonstrates that the convergence rate of the greedy randomized Kaczmarz method is much faster than the randomized Kaczmarz method, and numerical results also show that the greedy randomized Kaczmarz method is more efficient than the randomized Kaczmarz method.