Bivariate Lagrange interpolation at the Padua points: The generating curve approach

Authors:
Len Bos;Marco Caliari;Stefano De Marchi;Marco Vianello;Yuan Xu
Affiliations:
Department of Mathematics and Statistics, University of Calgary, Canada;Department of Pure and Applied Mathematics, University of Padua, Italy;Department of Computer Science, University of Verona, Italy;Department of Pure and Applied Mathematics, University of Padua, Italy;Department of Mathematics, University of Oregon, USA
Venue:
Journal of Approximation Theory
Year:
2006

Citing 4
Cited 13

Christoffel functions and Fourier series for multivariate orthogonal polynomials

Journal of Approximation Theory
Lagrange interpolation on Chebyshev points of two variables

Journal of Approximation Theory
A Numerical Study of the Xu Polynomial Interpolation Formula in Two Variables

Computing
On the Lebesgue constant for the Xu interpolation formula

Journal of Approximation Theory

Hyperinterpolation in the cube

Computers & Mathematics with Applications
Uniform approximation by discrete least squares polynomials

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
Computing approximate Fekete points by QR factorizations of Vandermonde matrices

Computers & Mathematics with Applications
Least-squares polynomial approximation on weakly admissible meshes: Disk and triangle

Journal of Computational and Applied Mathematics
A method to compute recurrence relation coefficients for bivariate orthogonal polynomials by unitary matrix transformations

Numerical Algorithms
Padua2DM: fast interpolation and cubature at the Padua points in Matlab/Octave

Numerical Algorithms
Computing Multivariate Fekete and Leja Points by Numerical Linear Algebra

SIAM Journal on Numerical Analysis
Full length articles: On the Lebesgue constant of Leja sequences for the unit disk and its applications to multivariate interpolation

Journal of Approximation Theory
Stability of kernel-based interpolation

Advances in Computational Mathematics
Computing Fekete and Lebesgue points: Simplex, square, disk

Journal of Computational and Applied Mathematics
Radial orthogonality and Lebesgue constants on the disk

Numerical Algorithms

Quantified Score

Hi-index	0.00

Visualization

Abstract

We give a simple, geometric and explicit construction of bivariate interpolation at certain points in a square (called Padua points), giving compact formulas for their fundamental Lagrange polynomials. We show that the associated norms of the interpolation operator, i.e., the Lebesgue constants, have minimal order of growth of O((logn)^2). To the best of our knowledge this is the first complete, explicit example of near optimal bivariate interpolation points.