The triangle method for finding the corner of the L-curve Original Research Article

The Conjugate Gradient Method (CG) has an intrinsic regularization property when applied to systems of linear equations with ill-conditioned matrices. This regularization property is specially useful when either the right-hand side or the coefficient matrix, or both are given with errors. The regularization parameter is the iteration number, and in order to find this parameter, the L-curve is used. Here we present a novel method to find the corner of the L-curve, that determines the regularizing iteration number. Numerical results on the collection of test problems [SIAM J. Sci. Comput. 16 (1995) 506–512] are given to illustrate the potentiality of the method.