Modified Iterative Runge-Kutta-Type Methods for Nonlinear Ill-Posed Problems. (1st December 2016)

• Record Type: Journal Article
• Authors: Pornsawad, Pornsarp; Böckmann, Christine
• Is Part Of: Numerical functional analysis and optimization. Volume 37:Number 12(2016)
• Page Start: 1562
• Page End: 1589
• Publication Date: 2016-12-01
• Subjects: Nonlinear ill-posed problems -- Runge-Kutta methods -- regularization methods -- Hölder-type source condition -- stopping rules; 65J15 -- 65J22 -- 47J25 -- 47J06; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1219744
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: This work is devoted to the convergence analysis of a modified Runge-Kutta-type iterative regularization method for solving nonlinear ill-posed problems under a priori and a posteriori stopping rules. The convergence rate results of the proposed method can be obtained under a Hölder-type sourcewise condition if the Fréchet derivative is properly scaled and locally Lipschitz continuous. Numerical results are achieved by using the Levenberg-Marquardt, Lobatto, and Radau methods.