An algorithm for estimating the optimal regularization parameter by the L-curve

Abstract

In this paper we introduce a new algorithm to estimate the optimal regularization parameter in truncated singular value decomposition (TSVD) regularization methods for the numerical solution of severely ill-posed linear systems. The algorithm couples a geometrical approach to identify the corner of the L-curve associated to the problem with some heuristic rules. Numerical results are reported to highlight the performance of the algorithm with respect to other methods for the selection of the regularization parameter.

Keywords

• ill-conditioned linear systems
• regularization
• truncated singular value decomposition (tsvd)
• l-curve