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Fast fully iterative Newton-type methods for inverse problems

2007
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Journal of Inverse and Ill-Posed Problems
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We study nonlinear inverse problems of the form F (x) = y , and their stable solution via iterative regularization methods, in particular by Newton-type methods, which are well-known for their fast convergence for well-posed problems. A basic step of Newton's method consists of calculating the update ∆x k via solution of a linearized equation ), which will in general be ill-posed if the nonlinear problem is. Thus, for ill-posed problems, the linearized equations have to be solved by some

doi:10.1515/jiip.2007.014
fatcat:ywbsvowp3rbnfpsqebia5xqab4