\texttt{Padua2DM}: Fast interpolation and cubature at the Padua points in \texttt{MATLAB/Octave}

DOI10.1007/s11075-010-9373-1zbMath1206.65028OpenAlexW2078574976MaRDI QIDQ621781

Alvise Sommariva, Stefano De Marchi, Marco Caliari, Marco Vianello

Publication date: 28 January 2011

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-010-9373-1

zbMATH Keywords

numerical examplesfast algorithmsfast Fourier transformLagrange interpolationalgebraic cubaturePadua points

Mathematics Subject Classification ID

Numerical interpolation (65D05) Multidimensional problems (41A63) Interpolation in approximation theory (41A05) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items

Bivariate Lagrange interpolation at the node points of non-degenerate Lissajous curves, Sensitivity Analysis for Stability of Uncertain Delay Differential Equations Using Polynomial Chaos Expansions, Multivariate polynomial interpolation on Lissajous-Chebyshev nodes, Padua points and fake nodes for polynomial approximation: old, new and open problems, Polynomial approximation on Lissajous curves in the \(d\)-cube, Uniform weighted approximation on the square by polynomial interpolation at Chebyshev nodes, A new collocation method using near-minimal Chebyshev quadrature nodes on a square, Accurate polynomial interpolation by using the Bernstein basis, On the numerical computation of bivariate Lagrange polynomials, A method to compute recurrence relation coefficients for bivariate orthogonal polynomials by unitary matrix transformations, Sum-of-Squares Optimization without Semidefinite Programming, Bivariate Lagrange interpolation at the node points of Lissajous curves -- the degenerate case, Cubature formulae for nearly singular and highly oscillating integrals, On the computation of sets of points with low Lebesgue constant on the unit disk, Padua2DM, Padua2D, Computing Fekete and Lebesgue points: Simplex, square, disk, Least squares problems involving generalized Kronecker products and application to bivariate polynomial regression

Uses Software

• Matlab
• Octave

Cites Work

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• A method for numerical integration on an automatic computer
• Improved cubature formulae of high degrees of exactness for the square
• Bivariate Lagrange interpolation at the Padua points: the generating curve approach
• Nontensorial Clenshaw-Curtis cubature
• New cubature formulae and hyperinterpolation in three variables
• Bivariate polynomial interpolation on the square at new nodal sets
• Bivariate Lagrange interpolation at the Padua points: The ideal theory approach
• Fast construction of the Fejér and Clenshaw-Curtis quadrature rules
• Is Gauss Quadrature Better than Clenshaw–Curtis?