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

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

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

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

Research Institute for Symbolic Computation

Research output: Working paper and reports › Research report

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.

Original language	English
Place of Publication	Linz
Publisher	DK Computational Mathematics, JKU
Number of pages	19
Publication status	Published - Dec 2011

Publication series

Name	DK Report Series
No.	2011-12

Fields of science

101001 Algebra
101002 Analysis
101 Mathematics
102 Computer Sciences
102011 Formal languages
101009 Geometry
101013 Mathematical logic
101020 Technical mathematics
101025 Number theory
101012 Combinatorics
101005 Computer algebra
101006 Differential geometry
101003 Applied geometry
102025 Distributed systems

JKU Focus areas

Computation in Informatics and Mathematics

Cite this

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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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T1 - Harmonic interpolation based on Radon projections along the sides of regular polygons

AU - Georgieva, Irina

AU - Hofreither, Clemens

AU - Koutschan, Christoph

AU - Pillwein, Veronika

AU - Thanatipanonda, Thotsaporn

PY - 2011/12

Y1 - 2011/12

N2 - 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.

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.

M3 - Research report

T3 - DK Report Series

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

PB - DK Computational Mathematics, JKU

CY - Linz

ER -