Regularization by discretization in Banach spaces

Uno Hämarik, Barbara Kaltenbacher, Urve Kangro, Elena Resmerita
2016 Inverse Problems  
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
more » ... pancy 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 space dimension.
doi:10.1088/0266-5611/32/3/035004 fatcat:l7xavu44szd2bjf5wfmjswbufi