MiKM: multi-step inertial Krasnosel’skiǐ-Mann algorithm and its applications. In this paper, we first introduce a multi-step inertial Krasnosel’skiǐ-Mann algorithm (MiKM) for nonexpansive operators in real Hilbert spaces. We give the convergence of the MiKM by investigating the convergence of the Krasnosel’skiǐ-Mann algorithm with perturbations. We also establish global pointwise and ergodic iteration complexity bounds of the Krasnosel’skiǐ-Mann algorithm with perturbations. Based on the MiKM, we construct some multi-step inertial splitting methods, including the multi-step inertial Douglas-Rachford splitting method (MiDRS), the multi-step inertial forward-backward splitting method, multi-step inertial backward-forward splitting method and and the multi-step inertial Davis-Yin splitting method. Numerical experiments are provided to illustrate the advantage of the MiDRS over the one-step inertial DRS and the original DRS.
Keywords for this software
References in zbMATH (referenced in 3 articles , 1 standard article )
Showing results 1 to 3 of 3.
- Hieu, Dang Van; Strodiot, Jean Jacques; Muu, Le Dung: An explicit extragradient algorithm for solving variational inequalities (2020)
- Dong, Q. L.; Huang, J. Z.; Li, X. H.; Cho, Y. J.; Rassias, Th. M.: MiKM: multi-step inertial Krasnosel’skiǐ-Mann algorithm and its applications (2019)
- Heaton, Howard; Censor, Yair: Asynchronous sequential inertial iterations for common fixed points problems with an application to linear systems (2019)