Journal of Scientific Computing

, Volume 63, Issue 1, pp 163–184 | Cite as

Simple and Efficient Determination of the Tikhonov Regularization Parameter Chosen by the Generalized Discrepancy Principle for Discrete Ill-Posed Problems

  • Fermín S. Viloche Bazán


Discrete ill-posed problems where both the coefficient matrix and the right hand side are contaminated by noise appear in a variety of engineering applications. In this paper we consider Tikhonov regularized solutions where the regularization parameter is chosen by the generalized discrepancy principle (GDP). In contrast to Newton-based methods often used to compute such parameter, we propose a new algorithm referred to as GDP-FP, where derivatives are not required and where the regularization parameter is calculated efficiently by a fixed-point iteration procedure. The algorithm is globally and monotonically convergent. Additionally, a specialized version of GDP-FP based on a projection method, that is well-suited for large-scale Tikhonov problems, is also proposed and analyzed in detail. Numerical examples are presented to illustrate the effectiveness of the proposed algorithms on test problems from the literature.


Discrete ill-posed problems Tikhonov regularization  Projection method Generalized discrepancy principle Noisy operator Noisy right hand side 


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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of MathematicsFederal University of Santa CatarinaFlorianópolisBrazil

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