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

DOI10.2478/s11533-012-0160-1zbMath1263.41002OpenAlexW2073745585MaRDI QIDQ1945349

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

Publication date: 8 April 2013

Published in: Central European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/s11533-012-0160-1

zbMATH Keywords

harmonic polynomialssymbolic computationcomputer tomographyRadon projectionsharmonic interpolation

Mathematics Subject Classification ID

Radon transform (44A12) Numerical interpolation (65D05) Multidimensional problems (41A63) Interpolation in approximation theory (41A05) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Related Items

ON THE LOWER BOUND IN THE PROBLEM OF APPROXIMATE RECONSTRUCTION OF FUNCTIONS BY VALUES OF THE RADON TRANSFORM, Interpolating solutions of the Poisson equation in the disk based on Radon projections, Interpolation of harmonic functions based on Radon projections, New results on regularity and errors of harmonic interpolation using Radon projections, On rank-deficiency in direct Trefftz method for 2D Laplace problems, Cubature rules for harmonic functions based on Radon projections

Uses Software

• HolonomicFunctions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Multivariate divided differences and multivariate interpolation of Lagrange and Hermite type
• Multivariate interpolation and the Radon transform
• The angles between the null spaces of X rays
• A holonomic systems approach to special functions identities
• The method of creative telescoping
• Hypergeometric solutions of linear recurrences with polynomial coefficients
• Optimal reconstruction of a function from its projections
• Numerical integration over a disc. A new Gaussian quadrature formula
• Uniqueness of the Gaussian quadrature for a ball
• On the reconstruction of a function on a circular domain from a sampling of its line integrals
• Smoothing of Radon projections type of data by bivariate polynomials
• The Mathematics of Computerized Tomography
• On Interpolation in the Unit Disk Based on Both Radon Projections and Function Values
• Surface Reconstruction and Lagrange Basis Polynomials
• Tomographic reconstruction with arbitrary directions
• Interpolation by bivariate polynomials based on Radon projections
• Advanced applications of the holonomic systems approach
• Reconstruction of a Polynomial from Its Radon Projections