Algorithm 886: Padua2D---Lagrange Interpolation at Padua Points on Bivariate Domains We present a stable and efficient Fortran implementation of polynomial interpolation at the Padua points on the square [ − 1,1]2. These points are unisolvent and their Lebesgue constant has minimal order of growth (log square of the degree). The algorithm is based on the representation of the Lagrange interpolation formula in a suitable orthogonal basis, and takes advantage of a new matrix formulation together with the machine-specific optimized BLAS subroutine for the matrix-matrix product. Extension to interpolation on rectangles, triangles and ellipses is also described (Source:

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 20 articles , 1 standard article )

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  1. Marco, Ana; Martínez, José-Javier; Viaña, Raquel: Least squares problems involving generalized Kronecker products and application to bivariate polynomial regression (2019)
  2. Meurant, Gérard; Sommariva, Alvise: On the computation of sets of points with low Lebesgue constant on the unit disk (2019)
  3. Papp, Dávid; Yildiz, Sercan: Sum-of-squares optimization without semidefinite programming (2019)
  4. Occorsio, Donatella; Serafini, Giada: Cubature formulae for nearly singular and highly oscillating integrals (2018)
  5. Bos, L.; De Marchi, S.; Vianello, M.: Polynomial approximation on Lissajous curves in the (d)-cube (2017)
  6. Dencker, Peter; Erb, Wolfgang: Multivariate polynomial interpolation on Lissajous-Chebyshev nodes (2017)
  7. Marco, Ana; Martínez, José-Javier; Viana, Raquel: Accurate polynomial interpolation by using the Bernstein basis (2017)
  8. Erb, Wolfgang: Bivariate Lagrange interpolation at the node points of Lissajous curves -- the degenerate case (2016)
  9. Erb, Wolfgang; Kaethner, Christian; Ahlborg, Mandy; Buzug, Thorsten M.: Bivariate Lagrange interpolation at the node points of non-degenerate Lissajous curves (2016)
  10. Fasshauer, Gregory; McCourt, Michael: Kernel-based approximation methods using MATLAB (2016)
  11. Poppe, Koen; Cools, Ronald: CHEBINT, a MATLAB/Octave toolbox for fast multivariate integration and interpolation based on Chebyshev approximations over hypercubes (2013)
  12. Briani, Matteo; Sommariva, Alvise; Vianello, Marco: Computing Fekete and Lebesgue points: Simplex, square, disk (2012)
  13. Bos, L.; Calvi, J.-P.; Levenberg, N.; Sommariva, A.; Vianello, M.: Geometric weakly admissible meshes, discrete least squares approximations and approximate Fekete points (2011)
  14. Caliari, Marco; De Marchi, Stefano; Sommariva, Alvise; Vianello, Marco: \textttPadua2DM: Fast interpolation and cubature at the Padua points in \textttMATLAB/Octave (2011)
  15. Van Barel, Marc; Chesnokov, Andrey: A method to compute recurrence relation coefficients for bivariate orthogonal polynomials by unitary matrix transformations (2010)
  16. Sommariva, Alvise; Vianello, Marco: Computing approximate Fekete points by QR factorizations of Vandermonde matrices (2009)
  17. Caliari, Marco; de Marchi, Stefano; Vianello, Marco: Bivariate Lagrange interpolation at the Padua points: Computational aspects (2008)
  18. Caliari, Marco; De Marchi, Stefano; Vianello, Marco: Algorithm 886: Padua2d---Lagrange interpolation at padua points on bivariate domains. (2008) ioport
  19. Sommariva, Alvise; Vianello, Marco; Zanovello, Renato: Nontensorial Clenshaw-Curtis cubature (2008)
  20. Bos, Len; Caliari, Marco; De Marchi, Stefano; Vianello, Marco; Xu, Yuan: Bivariate Lagrange interpolation at the Padua points: the generating curve approach (2006)