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Non-monotoneous parallel iteration for solving convex feasibility problems. (English) Zbl 1249.65040
Summary: The method of projections onto convex sets to find a point in the intersection of a finite number of closed convex sets in an Euclidean space, sometimes leads to slow convergence of the constructed sequence. Such slow convergence depends both on the choice of the starting point and on the monotonous behavior of the usual algorithms. As there is normally no indication of how to choose the starting point in order to avoid slow convergence, we present in this paper a non-monotonous parallel algorithm that may eliminate considerably the influence of the starting point.

65D18 Numerical aspects of computer graphics, image analysis, and computational geometry
65Y05 Parallel numerical computation
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