Convergence theorems for inertial KM-type algorithms

Authors:
Paul-Emile Maingé
Affiliations:
Département Scientifique Interfacultaire, Campus de Schoelcher, GRIMMAG, Université des Antilles-Guyane, 97230 Cedex, Martinique (F.W.I.), France
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

This paper deals with the convergence analysis of a general fixed point method which unifies KM-type (Krasnoselskii-Mann) iteration and inertial type extrapolation. This strategy is intended to speed up the convergence of algorithms in signal processing and image reconstruction that can be formulated as KM iterations. The convergence theorems established in this new setting improve known ones and some applications are given regarding convex feasibility problems, subgradient methods, fixed point problems and monotone inclusions.