Multivariate polynomial interpolation and sampling in Paley–Wiener spaces

On Lagrange multivariate interpolation problem in generalized degree polynomial spaces

The aim of this paper is to study the Lagrange multivariate interpolation problems in the space of polynomials of w-degree n. Some new results concerning the polynomial spaces of w-degree n are given. An algorithm for obtaining the w-minimal interpolation space is presented. Key–Words: Lagrange multivariate polynomial interpolation, whomogeneous polynomial spaces, Generalize degree.

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

Sampling theorem for polynomial interpolation

The classic polynomial interpolation approach is used to derive a sampling theorem for the class of signals that are the response of systems described by differential equations with constant coefficients. In particular, the polynomial that interpolates the signal between the sampling points for increasing order will give increasing accuracy for stable one-sided sequences, if the sampling rate i...

On the Error in Multivariate Polynomial Interpolation

Simple proofs are provided for two properties of a new multivariate polynomial interpolation scheme, due to Amos Ron and the author, and a formula for the interpolation error is derived and discussed.