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Regularized Quadrature Methods for Fredholm Integral Equations of the First Kind

  • Sergei V. Pereverzev
  • Evgeniya V. Semenova
  • Pavlo Tkachenko
Chapter

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.

Notes

Acknowledgements

This work was done while the second author was visiting Johann Radon Institute within the EU-Horizon 2020 MSC-RISE project AMMODIT.

The authors affiliated with Johann Radon Institute gratefully acknowledge the support of the Austrian Science Fund (FWF): project I1669.

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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Sergei V. Pereverzev
    • 1
  • Evgeniya V. Semenova
    • 2
  • Pavlo Tkachenko
    • 1
  1. 1.Johann Radon Institute for Computational and Applied MathematicsLinzAustria
  2. 2.Institute of Mathematics National Academy of Sciences of UkraineKyivUkraine

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