Arnoldi-Tikhonov regularization methods

Authors:
Bryan Lewis;Lothar Reichel
Affiliations:
Rocketcalc LLC, 100 W. Crain Ave., Kent, OH 44240, USA;Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

Tikhonov regularization for large-scale linear ill-posed problems is commonly implemented by determining a partial Lanczos bidiagonalization of the matrix of the given system of equations. This paper explores the possibility of instead computing a partial Arnoldi decomposition of the given matrix. Computed examples illustrate that this approach may require fewer matrix-vector product evaluations and, therefore, less arithmetic work. Moreover, the proposed range-restricted Arnoldi-Tikhonov regularization method does not require the adjoint matrix and, hence, is convenient to use for problems for which the adjoint is difficult to evaluate.