Three Results on Iterative Regularization
Abstract
In this paper we present three theorems which give insight into the
regularizing properties of {\minres}. While our theory does not
completely characterize the regularizing behavior of the algorithm, it
provides a partial explanation of the observed behavior of the method.
Unlike traditional attempts to explain the regularizing properties of
Krylov subspace methods, our approach focuses on convergence
properties of the residual rather than on convergence analysis of the
harmonic Ritz values. The import of our analysis is illustrated by
two examples. In particular, our theoretical and numerical results
support the following important observation: in some circumstances the
dimension of the optimal Krylov subspace can be much smaller than the
number of the components of the truncated spectral solution that must
be computed to attain comparable accuracy.
Also cross-referenced as UMIACS-TR-98-62