An iterative method for Tikhonov regularization with a general linear regularization operator

Tikhonov regularization is one of the most popular approaches to solve discrete ill-posed problems with error-contaminated data. A regularization operator and a suitable value of a regularization parameter have to be chosen. This paper describes an iterative method, based on Golub-Kahan bidiagonalization, for solving large-scale Tikhonov minimization problems with a linear regularization operator of general form. The regularization parameter is determined by the discrepancy principle. Computed examples illustrate the performance of the method. \nKey words. Discrete ill-posed problem, iterative method, Tikhonov regularization, general\nlinear regularization operator, discrepancy principle.