Unisolvency for multivariate polynomial interpolation in Coatmèlec configurations of nodes

Unisolvency for multivariate polynomial interpolation in Coatmèlec configurations of nodes

A new and straightforward proof of the unisolvability of the problem of multivariate polynomial interpolation based on Coatmèlec configurations of nodes, a class of properly posed set of nodes defined by hyperplanes, is presented. The proof generalizes a previous one for the bivariate case and is based on a recursive reduction of the problem to simpler ones following the so-called Radon-Bézout ...

Multivariate polynomial interpolation on Lissajous-Chebyshev nodes

In this contribution, we study multivariate polynomial interpolation and quadrature rules on non-tensor product node sets linked to Lissajous curves and Chebyshev varieties. After classifying multivariate Lissajous curves and the interpolation nodes related to these curves, we derive a discrete orthogonality structure on these node sets. Using this discrete orthogonality structure, we can deriv...

Approximating optimal point configurations for multivariate polynomial interpolation

Efficient and effective algorithms are designed to compute the coordinates of nearly optimal points for multivariate polynomial interpolation on a general geometry. “Nearly optimal” refers to the property that the set of points has a Lebesgue constant near to the minimal Lebesgue constant with respect to multivariate polynomial interpolation on a finite region. The proposed algorithms range fro...

On multivariate polynomial interpolation

We provide a map Θ 7→ ΠΘ which associates each finite set Θ of points in C with a polynomial space ΠΘ from which interpolation to arbitrary data given at the points in Θ is possible and uniquely so. Among all polynomial spaces Q from which interpolation at Θ is uniquely possible, our ΠΘ is of smallest degree. It is also Dand scale-invariant. Our map is monotone, thus providing a Newton form for...

Lectures on Multivariate Polynomial Interpolation