Convergence Rate Analysis of Inertial Krasnoselskii-Mann Type Iteration with Applications.

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 <inline-graphic></inline-graphic> 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. [ABSTRACT FROM AUTHOR]