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

Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Johannes Kepler University Linz

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

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
Externally published	Yes

Keywords

Computer tomography
Harmonic interpolation
Harmonic polynomials
Radon projections
Symbolic computation

Access to Document

10.2478/s11533-012-0160-1

Cite this

@article{6ea46635cb6344d9b84df0025764a7e0,

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.",

keywords = "Computer tomography, Harmonic interpolation, Harmonic polynomials, Radon projections, Symbolic computation",

author = "Irina Georgieva and Clemens Hofreither and Christoph Koutschan and Veronika Pillwein and Thotsaporn Thanatipanonda",

year = "2013",

doi = "10.2478/s11533-012-0160-1",

language = "English",

volume = "11",

pages = "609--620",

journal = "Central European Journal of Mathematics",

issn = "1895-1074",

publisher = "Versita",

number = "4",

}

TY - JOUR

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 - 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.

KW - Computer tomography

KW - Harmonic interpolation

KW - Harmonic polynomials

KW - Radon projections

KW - Symbolic computation

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

U2 - 10.2478/s11533-012-0160-1

DO - 10.2478/s11533-012-0160-1

M3 - Article

AN - SCOPUS:84873111371

SN - 1895-1074

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

Keywords

Access to Document

Other files and links

Fingerprint

Cite this