A partial multivariate polynomial interpolation problem

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...

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 partial polynomial interpolation

The Alexander-Hirschowitz theorem says that a general collection of k double points in P imposes independent conditions on homogeneous polynomials of degree d with a well known list of exceptions. We generalize this theorem to arbitrary zero-dimensional schemes contained in a general union of double points. We work in the polynomial interpolation setting. In this framework our main result says ...

Lectures on Multivariate Polynomial Interpolation

Computational aspects of multivariate polynomial interpolation

The paper is concerned with the practical implementation of two methods to compute the solution of polynomial interpolation problems. In addition to a description of the implementation, practical results and several improvements will be discussed, focusing on speed and robustness of the algorithms under consideration.