Convergence Rate Analysis of Inertial Krasnoselskii–Mann Type Iteration with Applications

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It is well known that the Krasnoselskii–Mann iteration of nonexpansive operators find applications in many areas of mathematics and known to be weakly convergent in the infinite dimensional setting. In this present paper, we provide a nonasymptotic convergence rate result for a Krasnoselskii–Mann iteration with inertial extrapolation step in real Hilbert spaces. We give some applications of our results to the Douglas–Rachford splitting method and the alternating projection method by John von Neumann. Our result serves as supplement to many existing results on convergence rate of Krasnoselskii–Mann iteration in the literature.