Weights in block iterative methods

Authors

Department of Mathematics, Iran University of Science and Technology, Tehran 16846-13114, Iran.

Abstract

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.