L-Curve and Curvature Bounds for Tikhonov Regularization

The L-curve is a popular aid for determining a suitable value of the regularization parameter when solving linear discrete ill-posed problems by Tikhonov regularization. However, the computational effort required to determine the L-curve and its curvature can be prohibitive for large-scale problems. Recently, inexpensively computable approximations of the L-curve and its curvature, referred to as the L-ribbon and the curvature-ribbon, respectively, were proposed for the case when the regularization operator is the identity matrix. This note discusses the computation and performance of the L- and curvature-ribbons when the regularization operator is an invertible matrix.