Optimal Convergence Rates Results for Linear Inverse Problems in Hilbert Spaces. (2nd February 2016)

• Record Type: Journal Article
• Authors: Albani, V.; Elbau, P.; de Hoop, M. V.; Scherzer, O.
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 5(2016)
• Page Start: 521
• Page End: 540
• Publication Date: 2016-02-02
• Subjects: Approximative source conditions -- convergence rates -- linear inverse problems -- regularization -- variational source conditions; 47A52 -- 49N45 -- 65J22; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1144070
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this article, we prove optimal convergence rates results for regularization methods for solving linear ill-posed operator equations in Hilbert spaces. The results generalizes existing convergence rates results on optimality to general source conditions, such as logarithmic source conditions. Moreover, we also provide optimality results under variational source conditions and show the connection to approximative source conditions.