Discrepancy principle for DSM II |
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| Institution: | 1. IBM, 76 Upper Ground, London SE1 9PZ, United Kingdom;2. IBM, P.O. Box 218, Yorktown Heights, NY 10598, USA;1. University of Belgrade, “Vinča” Institute of Nuclear Sciences, Laboratory for Theoretical and Condensed Matter Physics, P.O. BOX 522, 11001 Belgrade, Serbia;2. University of Belgrade, “Vinča” Institute of Nuclear Sciences, Laboratory for Nuclear and Plasma Physics, P.O. BOX 522, 11001 Belgrade, Serbia;3. Department of Physics, Faculty of Science, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Serbia;1. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China;2. State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha 410083, China;1. Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel;2. Department of Mathematics, Texas A&M University, 3368 TAMU, College Station, TX 77843-3368, USA;1. Università degli Studi di Napoli “Parthenope”, Via Parisi 13, 80100 Napoli, Italy;2. Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Via Cintia, 80126 Napoli, Italy |
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| Abstract: | Let Ay = f, A is a linear operator in a Hilbert space H, y ⊥ N(A) ≔ {u : Au = 0}, R(A) ≔ {h : h = Au, u ∈ D(A)} is not closed, ∥fδ − f∥ ⩽ δ. Given fδ, one wants to construct uδ such that limδ→0∥uδ − y∥ = 0. Two versions of discrepancy principles for the DSM (dynamical systems method) for finding the stopping time and calculating the stable solution uδ to the original equation Ay = f are formulated and mathematically justified. |
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