Several relaxed CQ-algorithms for the split feasibility problem with multiple output sets

In this paper, we present a pair of CQ-algorithms solving the split feasibility problem with multiple output sets and prove their strong convergence. Various methods are used in the algorithm to improve usability and increase the iteration speed. To broaden the algorithm's usability, we incorporate an adaptive stepsize and the algorithm works based on replacing the projection to the half-space with that to the intersection of two half-spaces. To hasten the convergence process, the"dividing by norm" approach is selected and the subsequent output hinges on the prior step's outcome. Finally, our numerical tests in signal recovery demonstrate the superior efficacy of our algorithms.