Reconfigurable Hardware Implementation of a Multivariate Polynomial Interpolation Algorithm

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...

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

A Smooth Multivariate Interpolation Algorithm

This brief paper introduces an algorithm for smooth interpolation of a multivariate function. The input data for the algorithm consists of a set of function values and derivatives up to order r on a finite set of points E. The algorithm utilizes the Voronoi diagram of E to construct a partition of unity that isolates the points of E. Averaging locally defined functions with the partition of uni...

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.