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Computation of discontinuous solutions of 2D linear ill-posed integral equations via adaptive grid regularization
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May 31, 2007
In this paper we apply the new regularization method adaptive grid regularization, which is well-suited for ill-posed problems with discontinuous solutions and which was introduced in an earlier paper [5], to 2D linear integral equations of the first kind. After describing the method we present some numerical examples showing that this method is a powerful tool to identify discontinuities in ill-posed problems.
Key Words: ill-posed problems,; integral equations,; regularization methods,; adaptive grid regularization,; adaptive grids.
Published Online: 2007-05-31
Published in Print: 2007-04-19
Copyright 2007, Walter de Gruyter
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Keywords for this article
ill-posed problems,;
integral equations,;
regularization methods,;
adaptive grid regularization,;
adaptive grids.
Articles in the same Issue
- Standard errors and confidence intervals in inverse problems: sensitivity and associated pitfalls
- Polynomial bases for subspaces of vector fields in the unit ball. Method of ridge functions
- A numerical method to solve an acoustic inverse scattering problem involving ghost obstacles
- On the analysis of distance functions for linear ill-posed problems with an application to the integration operator in L2
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- International Conferences Inverse Problems: Modeling and Simulation (Fethiye-Turkey), 2002, 2004, 2006
- International Conference Inverse and Ill-Posed Problems of Mathematical Physics dedicated to Professor M. M. Lavrent'ev on the occasion of his 75-th birthday August 20–25, 2007, Novosibirsk, Russia
