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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access January 29, 2013

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

Irina Georgieva, Clemens Hofreither, Christoph Koutschan, Veronika Pillwein and Thotsaporn Thanatipanonda
From the journal Open Mathematics

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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Published Online: 2013-1-29
Published in Print: 2013-4-1

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