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

Irina Georgieva; Clemens Hofreither; Christoph Koutschan; Veronika Pillwein; Thotsaporn Thanatipanonda

Open Mathematics (2013)

  • Volume: 11, Issue: 4, page 609-620
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Irina Georgieva, et al. "Harmonic interpolation based on Radon projections along the sides of regular polygons." Open Mathematics 11.4 (2013): 609-620. <http://eudml.org/doc/269634>.

@article{IrinaGeorgieva2013,
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.},
author = {Irina Georgieva, Clemens Hofreither, Christoph Koutschan, Veronika Pillwein, Thotsaporn Thanatipanonda},
journal = {Open Mathematics},
keywords = {Harmonic interpolation; Harmonic polynomials; Radon projections; Computer tomography; Symbolic computation; harmonic interpolation; harmonic polynomials; computer tomography; symbolic computation},
language = {eng},
number = {4},
pages = {609-620},
title = {Harmonic interpolation based on Radon projections along the sides of regular polygons},
url = {http://eudml.org/doc/269634},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Irina Georgieva
AU - Clemens Hofreither
AU - Christoph Koutschan
AU - Veronika Pillwein
AU - Thotsaporn Thanatipanonda
TI - Harmonic interpolation based on Radon projections along the sides of regular polygons
JO - Open Mathematics
PY - 2013
VL - 11
IS - 4
SP - 609
EP - 620
AB - 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.
LA - eng
KW - Harmonic interpolation; Harmonic polynomials; Radon projections; Computer tomography; Symbolic computation; harmonic interpolation; harmonic polynomials; computer tomography; symbolic computation
UR - http://eudml.org/doc/269634
ER -

References

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