A BLAS-3 Version of the QR Factorization with Column Pivoting
SIAM Journal on Scientific Computing
Tensor product Gauss-Lobatto points are Fekete points for the cube
Mathematics of Computation
An Algorithm for Computing Fekete Points in the Triangle
SIAM Journal on Numerical Analysis
An encyclopaedia of cubature formulas
Journal of Complexity
Rounding error analysis of the classical Gram-Schmidt orthogonalization process
Numerische Mathematik
Spectral Element Methods on Unstructured Meshes: Comparisons and Recent Advances
Journal of Scientific Computing
Bivariate Lagrange interpolation at the Padua points: The generating curve approach
Journal of Approximation Theory
Bivariate Lagrange interpolation at the Padua points: the ideal theory approach
Numerische Mathematik
A Cardinal Function Algorithm for Computing Multivariate Quadrature Points
SIAM Journal on Numerical Analysis
Uniform approximation by discrete least squares polynomials
Journal of Approximation Theory
Pseudometrics, distances and multivariate polynomial inequalities
Journal of Approximation Theory
Algorithm 886: Padua2D---Lagrange Interpolation at Padua Points on Bivariate Domains
ACM Transactions on Mathematical Software (TOMS)
Bivariate Lagrange interpolation at the Padua points: Computational aspects
Journal of Computational and Applied Mathematics
Gauss-Green cubature and moment computation over arbitrary geometries
Journal of Computational and Applied Mathematics
Spectral element methods on unstructured meshes: which interpolation points?
Numerical Algorithms
Computing Multivariate Fekete and Leja Points by Numerical Linear Algebra
SIAM Journal on Numerical Analysis
Computing Fekete and Lebesgue points: Simplex, square, disk
Journal of Computational and Applied Mathematics
On the generation of symmetric Lebesgue-like points in the triangle
Journal of Computational and Applied Mathematics
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We propose a numerical method (implemented in Matlab) for computing approximate Fekete points on compact multivariate domains. It relies on the search of maximum volume submatrices of Vandermonde matrices computed on suitable discretization meshes, and uses a simple greedy algorithm based on QR factorization with column pivoting. The method gives also automatically an algebraic cubature formula, provided that the moments of the underlying polynomial basis are known. Numerical tests are presented for the interval and the square, which show that approximate Fekete points are well suited for polynomial interpolation and cubature.