Bivariate Lagrange interpolation at the node points of non-degenerate Lissajous curves

DOI10.1007/s00211-015-0762-1zbMath1350.41008arXiv1411.7589OpenAlexW1853512291MaRDI QIDQ303642

Christian Kaethner, Thorsten M. Buzug, Mandy Ahlborg, Wolfgang Erb

Publication date: 22 August 2016

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.7589

zbMATH Keywords

Lagrange interpolationbivariate interpolationLissajous curves

Mathematics Subject Classification ID

Interpolation in approximation theory (41A05) Approximation by polynomials (41A10) Numerical methods for trigonometric approximation and interpolation (65T40) Fourier series and coefficients in several variables (42B05)

Related Items (14)

Multivariate polynomial interpolation on Lissajous-Chebyshev nodes ⋮ Mathematical analysis of the 1D model and reconstruction schemes for magnetic particle imaging ⋮ Polynomial interpolation on interlacingrectangular grids ⋮ Multivariate approximation at fake nodes ⋮ Rhodonea curves as sampling trajectories for spectral interpolation on the unit disk ⋮ Lebesgue constants for polyhedral sets and polynomial interpolation on Lissajous-Chebyshev nodes ⋮ Shape-Driven Interpolation With Discontinuous Kernels: Error Analysis, Edge Extraction, and Applications in Magnetic Particle Imaging ⋮ Regularized Quadrature Methods for Fredholm Integral Equations of the First Kind ⋮ Optimal Points for Cubature Rules and Polynomial Interpolation on a Square ⋮ Reconfigurable formations of quadrotors on Lissajous curves for surveillance applications ⋮ Bivariate Lagrange interpolation at the node points of Lissajous curves -- the degenerate case ⋮ On \(L_p\)-error of bivariate polynomial interpolation on the square ⋮ Asymptotics of the Lebesgue constants for bivariate approximation processes ⋮ Mapped polynomials and discontinuous kernels for Runge and Gibbs phenomena

Uses Software

• Padua2DM
• Hyper2d
• Padua2D
• Algorithm 792
• CHEBINT
• LS2Ditp

Cites Work

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• \texttt{Padua2DM}: Fast interpolation and cubature at the Padua points in \texttt{MATLAB/Octave}
• Chebyshev lattices, a unifying framework for cubature with Chebyshev weight function
• A numerical study of the xu polynomial interpolation formula in two variables
• Bivariate Lagrange interpolation at the Padua points: the generating curve approach
• Hyper2d: A numerical code for hyperinterpolation on rectangles
• Bivariate Lagrange interpolation at the Padua points: Computational aspects
• Lagrange interpolation on Chebyshev points of two variables
• Kubaturformeln mit minimaler Knotenzahl
• There are infinitely many Lissajous knots
• On the history of multivariate polynomial interpolation
• Bivariate polynomial interpolation on the square at new nodal sets
• Polynomial interpolation in several variables
• Bivariate Lagrange interpolation at the Padua points: The ideal theory approach
• On the Lebesgue constant for the Xu interpolation formula
• Bivariate Polynomial Interpolation at the Geronimus Nodes
• Scattered Data Interpolation: Tests of Some Method
• Construction of Algebraic Cubature Rules Using Polynomial Ideal Theory
• LISSAJOUS KNOTS
• Algorithm 792

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