A Cyclic Douglas–Rachford Iteration Scheme |
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Authors: | Jonathan M Borwein Matthew K Tam |
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Institution: | 1. CARMA Centre, University of Newcastle, Callaghan, NSW, 2308, Australia
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Abstract: | In this paper, we present two Douglas–Rachford inspired iteration schemes which can be applied directly to N-set convex feasibility problems in Hilbert space. Our main results are weak convergence of the methods to a point whose nearest point projections onto each of the N sets coincide. For affine subspaces, convergence is in norm. Initial results from numerical experiments, comparing our methods to the classical (product-space) Douglas–Rachford scheme, are promising. |
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