On Multivariate Interpolation

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 Multivariate Lagrange Interpolation

Lagrange interpolation by polynomials in several variables is studied through a finite difference approach. We establish an interpolation formula analogous to that of Newton and a remainder formula, both of them in terms of finite differences. We prove that the finite difference admits an integral representation involving simplex spline functions. In particular, this provides a remainder formul...

On Multivariate Interpolation by Weights

The aim of this paper is to study a particular bivariate interpolation problem, named interpolation by weights. A minimal interpolation space is derived for these interpolation conditions. An integral formula for the remainder is given, as well as a superior bound for it. An expression for g(D)(Ln(f)) is obtained.

On Multivariate Birkhoff Rational Interpolation

Lectures on Multivariate Polynomial Interpolation