Two-step inertial accelerated algorithms for solving split feasibility problem with multiple output sets

In this paper, we present and study two new two-step inertial accelerated algorithms for finding an approximate solution of split feasibility problems with multiple output sets. Our methods are extensions of CQ algorithms previously studied in the literature. In contrast to the related iterative methods for solving SFP, our methods incorporate a two-step inertial technique that speeds up the convergence rate of the generated sequences to the unique solution of SFP studied in this work. Furthermore, we present weak and strong convergence results where the strong convergence result of our method is obtained without the on-line rule, a feature absent in related algorithms in the literature. Finally, we demonstrate the applicability and performance of our algorithms through numerical experiments. Our numerical results reveal that our methods perform better than existing related methods in the literature. •We proposed two-step inertial accelerated algorithms for solving split feasibility problems with multiple output set. It was shown that the iterative sequences generated by the one-step inertial fixed-point iteration may fail to provide acceleration. But, as shown by recent authors in the literature incorporating the multi-step inertial, like the two-step inertial could resolve the issue of not providing acceleration.•We proved the weak and strong convergence of our proposed algorithms, moreover, we achieved strong convergence result without the application of on-line rule, which is in contrast to the method studied in the literature.•We show the performance of our methods in relation to other already established methods in the framework through numerical experiments.