Iterative methods for solving the multiple-sets split feasibility problem with splitting self-adaptive step size

We introduce an iterative algorithm for solving the multiple-sets split feasibility problem with splitting self-adaptive step size. This step size is calculated directly from the iteration process without need to know the spectral norm of linear operators. We also generalize the chosen step size to a relaxed iterative algorithm. Theoretical convergence is proved in an infinite dimensional Hilbert space. Some numerical experiments are presented to verify the effectiveness of our proposed methods.