A fast subspace optimization method for nonlinear inverse problems in Banach spaces with an application in parameter identification. (22nd June 2018)

• Record Type: Journal Article
• Authors: Wald, Anne
• Is Part Of: Inverse problems. Volume 34:Number 8(2018:Aug.)
• Publication Date: 2018-06-22
• Subjects: nonlinear inverse problems -- Bregman projections -- duality mappings -- sequential subspace optimization -- regularization methods -- parameter identification; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aac8f3
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We introduce and analyze a fast iterative method based on sequential Bregman projections for nonlinear inverse problems in Banach spaces. The key idea, in contrast to the standard Landweber method, is to use multiple search directions per iteration in combination with a regulation of the step width in order to reduce the total number of iterations. This method is suitable for both exact and noisy data. In the latter case, we obtain a regularization method. An algorithm with two search directions is used for the numerical identification of a parameter in an elliptic boundary value problem.