Regularization by discretization in Banach spaces. (15th February 2016)

• Record Type: Journal Article
• Authors: Hämarik, Uno; Kaltenbacher, Barbara; Kangro, Urve; Resmerita, Elena
• Is Part Of: Inverse problems. Volume 32:Number 3(2016:Mar.)
• Publication Date: 2016-02-15
• Subjects: 02.30.Zz -- 02.30.Rz -- 02.60.Cb; regularization -- projections -- convergence analysis -- Volterra integral equations; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/0266-5611/32/3/035004
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We consider ill-posed linear operator equations with operators acting between Banach spaces. For solution approximation, the methods of choice here are projection methods onto finite dimensional subspaces, thus extending existing results from Hilbert space settings. More precisely, general projection methods, the least squares method and the least error method are analyzed. In order to appropriately choose the dimension of the subspace, we consider a priori and a posteriori choices by the discrepancy principle and by the monotone error rule. Analytical considerations and numerical tests are provided for a collocation method applied to a Volterra integral equation in one-dimension space.