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

Authors:
Barbara Kaltenbacher
Affiliations:
SFB013 Numerical and Symbolic Scientific Computing, University of Linz, Freitaedter-Strasse 313, A-4040 Linz, Austria
Venue:
Mathematics of Computation
Year:
2003

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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.