On Radon’s recipe for choosing correct sites for multivariate polynomial interpolation

On Radon's recipe for choosing correct sites for multivariate polynomial interpolation

A class of sets correct for multivariate polynomial interpolation is defined and verified, and shown to coincide with the collection of all correct sets constructible by the recursive application of Radon’s recipe, and a recent concrete recipe for correct sets is shown to produce elements in that class.

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 Error Formulas for Multivariate Polynomial Interpolation

In this paper we prove that the existence of an error formula of a form suggested in [2] leads to some very specific restrictions on an ideal basis that can be used in such formulas. As an application, we provide a negative answer to one version of the question posed by Carl de Boor (cf. [2]) regarding the existence of certain minimal error formulas for multivariate interpolation. §

Lectures on Multivariate Polynomial Interpolation

Quantum algorithm for multivariate polynomial interpolation

How many quantum queries are required to determine the coefficients of a degree-d polynomial in n variables? We present and analyse quantum algorithms for this multivariate polynomial interpolation problem over the fields [Formula: see text], [Formula: see text] and [Formula: see text]. We show that [Formula: see text] and [Formula: see text] queries suffice to achieve probability 1 for [Formul...