A new L-curve for ill-posed problems

Authors:
Lothar Reichel;Hassane Sadok
Affiliations:
Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA;Laboratoire de Mathématiques Pures et Appliquées, Université du Littoral, Centre Universtaire de la Mi-Voix, Bítiment H. Poincarré, 50 Rue F. Buisson, BP 699, 62228 Calais ...
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

The truncated singular value decomposition is a popular method for the solution of linear ill-posed problems. The method requires the choice of a truncation index, which affects the quality of the computed approximate solution. This paper proposes that an L-curve, which is determined by how well the given data (right-hand side) can be approximated by a linear combination of the first (few) left singular vectors (or functions), be used as an aid for determining the truncation index.