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A Weighted GCV Method for Lanczos Hybrid Regularization

Published

Author(s)

Julianne Chung, James G. Nagy, Dianne M. O'Leary

Abstract

Lanczos-hybrid regularization methods have been proposed as effective approaches for solving large-scale ill-posed inverse problems. Lanczos methods restrict the solution to lie in a Krylov subspace, but they are hindered by semi-convergence 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. In this paper we describe a weighted generalized cross validation (W-GCV) method for choosing the parameter. Using this method we demonstrate that the semi-convergence behavior of the Lanczos method can be overcome, making the solution less sensitive to the number of iterations.
Citation
Electronic Transactions on Numerical Analysis
Volume
28

Keywords

generalized cross validation, ill-posed problems, iterative methods, Lanczos bidiagonalization, LSQR, regularization, Tikhonov

Citation

Chung, J. , Nagy, J. and O'Leary, D. (2008), A Weighted GCV Method for Lanczos Hybrid Regularization, Electronic Transactions on Numerical Analysis, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=51142 (Accessed February 20, 2024)
Created January 14, 2008, Updated October 12, 2021