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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Volume 11, Issue 4

Issues

Volume 13 (2015)

Harmonic interpolation based on Radon projections along the sides of regular polygons

Irina Georgieva
  • Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl. 8, 1113, Sofia, Bulgaria
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/ Clemens Hofreither / Christoph Koutschan
  • Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenberger Str. 69, 4040, Linz, Austria
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/ Veronika Pillwein
  • Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenberger Str. 69, 4040, Linz, Austria
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/ Thotsaporn Thanatipanonda
  • Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenberger Str. 69, 4040, Linz, Austria
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Published Online: 2013-01-29 | DOI: https://doi.org/10.2478/s11533-012-0160-1

Abstract

Given information about a harmonic function in two variables, consisting of a finite number of values of its Radon projections, i.e., integrals along some chords of the unit circle, we study the problem of interpolating these data by a harmonic polynomial. With the help of symbolic summation techniques we show that this interpolation problem has a unique solution in the case when the chords form a regular polygon. Numerical experiments for this and more general cases are presented.

MSC: 41A05; 41A63; 44A12; 33F10; 65D05

Keywords: Harmonic interpolation; Harmonic polynomials; Radon projections; Computer tomography; Symbolic computation

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About the article

Published Online: 2013-01-29

Published in Print: 2013-04-01


Citation Information: Open Mathematics, Volume 11, Issue 4, Pages 609–620, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-012-0160-1.

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