Work

Projected iterated Tikhonov in general form with adaptive choice of the regularization parameter

Year: 2025

Type: article

Abstract: Tikhonov regularization is commonly used in the solution of linear discrete ill-posed problems. It is known that iterated Tikhonov regularization often produces approximate solutions of higher quality than (standard) Tikhonov regularization. This paper discusses iterated Tikhonov regularization for large-scale problems with a general regularization matrix. Specifically, the original problem is reduced to small size by application of a fairly small number of steps of the Arnoldi or Golub-Kahan processes, and iterated Tikhonov is applied to the reduced problem. The regularization parameter is determined by using an extension of a technique first described by Donatelli and Hanke for quite special coefficient matrices. Convergence of the method is established and computed examples illustrate its performance.

Source: Numerical Algorithms

DOI: 10.1007/s11075-025-02072-2

Authors: Alessandro Buccini, Silvia Gazzola, Lucas Onisk, Mirjeta Pasha, Lothar Reichel

Institutions: University of Cagliari, University of Pisa, Emory University, Virginia Tech, Kent State University

Language: English

Topic: Numerical methods in inverse problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Università degli Studi di Cagliari, Gruppo Nazionale per il Calcolo Scientifico