A New Gradient Method for Ill-Posed Problems. (26th April 2018)

• Record Type: Journal Article
• Authors: Neubauer, Andreas
• Is Part Of: Numerical functional analysis and optimization. Volume 39:Number 6(2018)
• Page Start: 737
• Page End: 762
• Publication Date: 2018-04-26
• Subjects: Discrepancy principle -- gradient methods -- Landweber iteration -- Linear and nonlinear ill-posed problems -- minimal error method -- steepest descent method -- stopping rule; 65J20 -- 65R30 -- 47J06 -- 47A52; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1414061
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: In this paper, we present a new gradient method for linear and nonlinear ill-posed problems F ( x ) = y . Combined with the discrepancy principle as stopping rule it is a regularization method that yields convergence to an exact solution if the operator F satisfies a tangential cone condition. If the exact solution satisfies smoothness conditions, then even convergence rates can be proven. Numerical results show that the new method in most cases needs less iteration steps than Landweber iteration, the steepest descent or minimal error method.