Research Stability of Parallel Algorithm for Solving Strong Separability Problem Based on Fejer Mappings

The problem of strong separating has an important role in the pattern recognition theory. The problem of strong separating means separating two convex non-intersected polyhedrons by the layer of maximum thickness. In this article, the non-stationary problems of strong separating are considered. Non-stationary problem is a problem for which the input data have been changed during the calculation process. An algorithm solving the non-stationary problem of strong separating must have two properties: auto-correcting and stability. Auto-correcting means the algorithm can continue its work effectively after the input data have been changed. Stability implies a small input data change implies a small deviation of the result. The auto-correcting is the feature of iterative algorithm based on Fejer processes. In the paper, the parallel algorithm based on Fejer mappings is described. This algorithm admits an effective implementation for the massively parallel multiprocessor systems. The notion of stable Fejer mapping is introduced. The theorem about stable Fejer mapping is proved.