Abstract
Fredholm equations of the first kind are very important in the mathematical formulation of inverse problems. The solution of such equations is an ill-posed problem, so that its numerical treatment requires special attention. The algorithm proposed here to solve first kind Fredholm equations is based on optimization and multigrid methods. That is the Fredholm equation is discretized, the resulting problem is reformulated as an optimization problem and solved several times. Every time the discretization, that is the grid, is refined and the solutions previously obtained on the coarser grids are used to reformulate the problem on the finer grid. The algorithm is tested on two inverse scattering problems. Results obtained both with synthetic and experimental data are reported.
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© 1998 Kluwer Academic Publishers, Boston
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Maponi, P., Misici, L., Zirilli, F. (1998). The Use of Optimization and Multiresolution Techniques for the Numerical Solution of First Kind Fredholm Equations. In: De Leone, R., Murli, A., Pardalos, P.M., Toraldo, G. (eds) High Performance Algorithms and Software in Nonlinear Optimization. Applied Optimization, vol 24. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3279-4_17
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DOI: https://doi.org/10.1007/978-1-4613-3279-4_17
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