HyBR
Hybrid Bidiagonalization Regularization
 Background

Lanczoshybrid regularization methods have been proposed as
effective approaches for solving largescale illposed inverse
problems.
Lanczos methods restrict the solution to lie in a
Krylov subspace, but they are hindered by semiconvergence
behavior, in that the quality of the solution first increases
and then decreases.
Hybrid methods apply a standard
regularization technique, such as Tikhonov regularization,
to the projected problem at each iteration.
Thus, regularization in hybrid methods is achieved both by Krylov filtering
and by appropriate choice of a regularization parameter
at each iteration.
 HyBR Implementation

Here we provide a MATLAB implementation of the Lanczoshybrid regularization,
which we refer to as HyBR.

The software for this may be obtained from:

Included with the above archives are examples:
We are grateful to
Professor Per Christian Hansen
for allowing us to include Regularization Tools
with our codes.

In our implementation, we use a "weighted GCV" scheme to choose
regularization parameters. A discussion of our approach is
given in:
J. Chung
,
J. Nagy
, and
D. O'Leary
,
A Weighted GCV Method for Lanczos Hybrid Regularization,
Emory Unviersity, Math/CS Technical Report TR2007004A.
(pdf version of paper)
 Acknowledgements

This work has been supported by the National Science Foundation
under Grants DMS 0511454 and CCF 0514214, and by the
DOE under a Computational Sciences Graduate Research Fellowship.
Any opinions, findings, and conclusions
or recommendations expressed in this material are those of the
author(s) and do not necessarily reflect
the views of the National Science Foundation or the Department of
Energy.