Viscosity modification with inertial forward-backward splitting methods for solving inclusion problems

Abstract

© Springer Nature Switzerland AG 2020. In this paper, we introduce the two new different modified forward-backward algorithms combining the viscosity approximation method with the inertial technical term for solving the inclusion problem. The strongly convergent theorems are established under some suitable conditions in Hilbert spaces. The application of algorithms in this study work is use to find the minimum-norm least-squares solution of an unconstrained linear system and test some numerical experiments. Moreover, the efficiency and the implementation of our methods have been shown through the examples.