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

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

doi:10.2478/s11533-012-0160-1

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: Contribution to journal › Article › peer-review

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
Pages (from-to)	609-620
Number of pages	12
Journal	Central European Journal of Mathematics
Volume	11
Issue number	4
DOIs	https://doi.org/10.2478/s11533-012-0160-1
Publication status	Published - 2013

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

Access to Document

10.2478/s11533-012-0160-1

Cite this

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title = "Harmonic interpolation based on Radon projections along the sides of regular polygons",

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 and Clemens Hofreither and Christoph Koutschan and Veronika Pillwein and Thotsaporn Thanatipanonda",

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AU - Georgieva, Irina

AU - Hofreither, Clemens

AU - Koutschan, Christoph

AU - Pillwein, Veronika

AU - Thanatipanonda, Thotsaporn

PY - 2013

Y1 - 2013

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.

UR - https://www.scopus.com/pages/publications/84873111371

U2 - 10.2478/s11533-012-0160-1

DO - 10.2478/s11533-012-0160-1

M3 - Article

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VL - 11

SP - 609

EP - 620

JO - Central European Journal of Mathematics

JF - Central European Journal of Mathematics

IS - 4

ER -

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

Abstract

Fields of science

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