Regularization Algorithms Based on Total Least Squares
Regularization Algorithms Based on Total Least Squares
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Date
1998-10-15
Authors
Hansen, Per Christian
O'Leary, Dianne P.
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Abstract
Discretizations of inverse problems lead to systems of linear equations
with a highly ill-conditioned coefficient matrix, and in order to
compute stable solutions to these systems it is necessary to apply
regularization methods.
Classical regularization methods, such as Tikhonov's method or
truncated {\em SVD}, are not designed for problems in which both the
coefficient matrix and the right-hand side are known only approximately.
For this reason, we develop {\em TLS}\/-based
regularization methods that take this situation into account.
Here, we survey two different approaches to incorporation of
regularization, or stabilization, into the {\em TLS} setting.
The two methods are similar in spirit to Tikhonov regularization
and truncated {\em SVD}, respectively.
We analyze the regularizing properties of the methods and
demonstrate by numerical examples that in certain cases with
large perturbations, these
new methods are able to yield more accurate regularized solutions than
those produced by the standard methods.
(Also cross-referenced as UMIACS-TR-96-65)