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V-cycle convergence of some multigrid methods for ill-posed problems


Author: Barbara Kaltenbacher
Journal: Math. Comp. 72 (2003), 1711-1730
MSC (2000): Primary 65J20, 65R30, 65N55
DOI: https://doi.org/10.1090/S0025-5718-03-01533-3
Published electronically: May 1, 2003
MathSciNet review: 1986801
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Abstract: For ill-posed linear operator equations we consider some V-cycle multigrid approaches, that, in the framework of Bramble, Pasciak, Wang, and Xu (1991), we prove to yield level independent contraction factor estimates. Consequently, we can incorporate these multigrid operators in a full multigrid method, that, together with a discrepancy principle, is shown to act as an iterative regularization method for the underlying infinite-dimensional ill-posed problem. Numerical experiments illustrate the theoretical results.


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Additional Information

Barbara Kaltenbacher
Affiliation: SFB013 Numerical and Symbolic Scientific Computing, University of Linz, Freitaedterstrasse 313, A-4040 Linz, Austria
Email: barbara.kaltenbacher@sfb013.uni-linz.ac.at

DOI: https://doi.org/10.1090/S0025-5718-03-01533-3
Keywords: Ill-posed problem, multigrid methods
Received by editor(s): November 21, 2000
Received by editor(s) in revised form: April 11, 2002
Published electronically: May 1, 2003
Additional Notes: The author was supported by the Fonds zur Förderung der wissenschaftlichen Forschung under grant T 7-TEC and project F1308 within Spezialforschungsbereich F013
Article copyright: © Copyright 2003 American Mathematical Society

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