Weights in block iterative methods

In this paper we introduce a sequential block iterative method and its simultaneous version with op- timal combination of weights (instead of convex combination) for solving convex feasibility problems. When the intersection of the given family of convex sets is nonempty, it is shown that any sequence generated by the given algorithms converges to a feasible point. Additionally for linear feasibility problems, we give equivalency of our algorithms with sequential and simultaneous block Kaczmarz methods explaining the optimal weights have been inherently used in Kaczmarz methods. In addi- tion, a convergence result is presented for simultaneous block Kaczmarz for the case of inconsistent linear system of equations.