A Convergence Analysis of the Iterated Lavrentiev Regularization Method under a Lipschitz Condition. (25th January 2022)

• Record Type: Journal Article
• Authors: Mahale, Pallavi; Singh, Ankit
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 2(2022)
• Page Start: 181
• Page End: 220
• Publication Date: 2022-01-25
• Subjects: Iterated lavrentiev regularization; lipschitz condition; monotone operator; nonlinear ill-posed operator equations; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2021.2021421
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: Mahale and Nair (2009) considered a iterated Lavrentive regularization method for obtaining stable approximate solution of nonlinear ill-posed operator equation F ( x ) = y, where F : D ( F ) ⊂ X → X is a nonlinear monotone operator on Hilbert space X . In this paper, we do convergence analysis of the method under the weaker non-linearity condition than the one considered by Mahale and Nair. We obtain convergence and rate of convergence results for the method merely under Lipschitz's condition. At the end of the paper, we give a numerical example to demonstrate our algorithm.