Choosing Regularization Parameters in Iterative Methods for Ill-Posed
Problems
Choosing Regularization Parameters in Iterative Methods for Ill-Posed
Problems
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Date
1998-10-15
Authors
Kilmer, Misha E.
O'Leary, Dianne P.
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Abstract
Numerical solution of ill-posed problems is often accomplished by
discretization (projection onto a finite dimensional subspace) followed by
regularization. If the discrete problem has high dimension, though,
typically we compute an approximate solution by projection onto an even
smaller dimensional space, via iterative methods based on Krylov
subspaces. In this work we present efficient algorithms that regularize
after this second projection rather than before it. We prove some results
on the approximate equivalence of this approach to other forms of
regularization and we present numerical examples.
(Also cross-referenced as UMIACS-TR-98-48)