A new greedy Kaczmarz algorithm for the solution of very large linear systems.

Abstract We propose a new greedy Kaczmarz algorithm for the solution of very large systems of linear equations. In our proposed algorithm, control sequence is determined by a greedy rule, and relaxation parameters are determined adaptively. Convergence of our proposed algorithm is proved. Numerical results show that the proposed algorithm is feasible and has faster convergence rate than the greedy randomized Kaczmarz algorithm. [ABSTRACT FROM AUTHOR]