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

Irina Georgieva 1 , Clemens Hofreither 2 , Christoph Koutschan 3 , Veronika Pillwein 3 , and Thotsaporn Thanatipanonda 3
  • 1 Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev, Bl. 8, 1113, Sofia, Bulgaria
  • 2 Doctoral College Computational Mathematics, Johannes Kepler University, Altenberger Str. 69, 4040, Linz, Austria
  • 3 Research Institute for Symbolic Computation (RISC), Johannes Kepler University, Altenberger Str. 69, 4040, Linz, Austria

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.

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