Two-grid iterative methods for ill-posed problems

by Michael Jacobsen

IMM M.Sc. Thesis 27-2000

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Abstract:
Two-grid methods for regularized inverse problems, proposed by Hanke and Vogel [Numerische Matematik, 83:385--402, 1999], are investigated. The derivation of the methods are treated in detail and the algorithms are tested extensively. An important quantity is a subspace splitting and appropriate subspace splittings is discussed. The algorithms are applied to both small problems in order to investigate the impact on, e.g. the condition number and to large problems in order to see the results for some real world problems.

Keywords:
conjugate gradients, preconditioning, ill-posed problem, ill-conditioned, regularization, two-grid

Dansk abstract:
To-nivau metoder til regulariserede inverse problemer, som foreslået af Hanke og Vogel [Numerische Matematik, 83:385--402, 1999], er undersøgt. Udledningen af metoderne er gennemgået i detaljer, og algoritmerne er testet grundigt. I algoritmerne indgår en underrumsopdeling, og flere anvendelige opdelinger er undersøgt. Algoritmerne er anvendt i forbindelse med læsning af både små og store problemer for både at få overskuelige resultater i forbindelse med for eksempel konditionstallet og for at se resultater for realistiske problemer.

Last update 4-9-2000 by fkc