Tikhonov regularization of large linear problems
The authors present a new numerical method for computing regularized solutions of Tikhonov regularization applied to large scale discrete linear ill-posed problems. The method is based on Lanczos bidiagonalization and Gauss quadrature. For choosing the regularization parameter the discrepancy principle is used. In addition to some details concerning the numerical analysis of the approach a comprehensive case study for Fredholm integral equations is presented. The results are compared with those of fast conjugate-gradient-based methods for Tikhonov regularization introduced by \textit{A. Frommer} and \textit{P. Maass} [SIAM J. Sci. Comput. 20, 1831--1850 (1999; Zbl 0943.65068)]. The authors note that the new method is able to reduce the number of matrix-vector product evaluations.
scientific article; zbMATH DE number 2012826