Regularized Quadrature Methods for Fredholm Integral Equations of the First Kind

Sergei V. Pereverzev (), Evgeniya V. Semenova and Pavlo Tkachenko ()
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Sergei V. Pereverzev: Johann Radon Institute for Computational and Applied Mathematics
Evgeniya V. Semenova: Institute of Mathematics National Academy of Sciences of Ukraine
Pavlo Tkachenko: Johann Radon Institute for Computational and Applied Mathematics

A chapter in Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan, 2018, pp 1017-1034 from Springer

Abstract: Abstract Although quadrature methods for solving ill-posed integral equations of the first kind were introduced just after the publication of the classical papers on the regularization by A.N. Tikhonov and D.L. Phillips, there are still no known results on the convergence rate of such discretization. At the same time, some problems appearing in practice, such as Magnetic Particle Imaging (MPI), allow one only a discretization corresponding to a quadrature method. In the present paper we study the convergence rate of quadrature methods under general regularization scheme in the Reproducing Kernel Hilbert Space setting.

Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-72456-0_45

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DOI: 10.1007/978-3-319-72456-0_45

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