Range-relaxed criteria for choosing the Lagrange multipliers in nonstationary iterated Tikhonov method. (29th October 2018)

• Record Type: Journal Article
• Authors: Boiger, R; Leitão, A; Svaiter, B F
• Is Part Of: IMA journal of numerical analysis. Volume 40:Number 1(2020)
• Page Start: 606
• Page End: 627
• Publication Date: 2018-10-29
• Subjects: ill-posed problems -- linear operators -- iterated Tikhonov method -- nonstationary methods; Numerical analysis -- Periodicals; 519.405
• DOI: 10.1093/imanum/dry066
• Languages: English
• ISSNs: 0272-4979

Abstract

Abstract: In this article we propose a novel nonstationary iterated Tikhonov (NIT)-type method for obtaining stable approximate solutions to ill-posed operator equations modeled by linear operators acting between Hilbert spaces. Geometrical properties of the problem are used to derive a new strategy for choosing the sequence of regularization parameters (Lagrange multipliers) for the NIT iteration. Convergence analysis for this new method is provided. Numerical experiments are presented for two distinct applications: (I) a two-dimensional elliptic parameter identification problem (inverse potential problem); and (II) an image-deblurring problem. The results obtained validate the efficiency of our method compared with standard implementations of the NIT method (where a geometrical choice is typically used for the sequence of Lagrange multipliers).