A Pre-Conditioning CQ Algorithm with Double Inertia and Self-Updated Stepsizes for Split Feasibility Problems in Hilbert Spaces

In this work, we propose a double inertial pre-conditioning CQ Algorithm for split feasibility problem in real Hilbert spaces, in which, we use the double inertial steps and new stepsizes to speed up the convergent rate. We also compute the only one projection onto the nonempty closed convex set C in our proposed method. These help improve the numerical results. Next, we establish the weak convergence of the sequence generated by our method. Finally, we use a numerical experiment to demonstrate our theoretical results.