On projective Landweber–Kaczmarz methods for solving systems of nonlinear ill-posed equations. (11th January 2016)

• Record Type: Journal Article
• Authors: Leitão, A; Svaiter, B F
• Is Part Of: Inverse problems. Volume 32:Number 2(2016:Feb.)
• Publication Date: 2016-01-11
• Subjects: Ill-posed problems -- nonlinear equations -- Landweber method -- Kaczmarz method -- projective method; 65J20 -- 47J06; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/2/025004
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: In this article we combine the projective Landweber method, recently proposed by the present authors, with Kaczmarz's method for solving systems of nonlinear ill-posed equations. The underlying assumption used in this work is the tangential cone condition. We show that the proposed iteration is a convergent regularization method. Numerical tests are presented for a nonlinear inverse problem related to the Dirichlet-to-Neumann map, indicating a superior performance of the proposed method when compared with other well established iterations. Our preliminary investigation indicates that the resulting iteration is a promising alternative for computing stable solutions of large scale systems of nonlinear ill-posed equations .