Multivariate polynomial interpolation on lower sets

Multivariate polynomial interpolation on lower sets

In this paper we study multivariate polynomial interpolation on lower sets of points. A lower set can be expressed as the union of blocks of points. We show that a natural interpolant on a lower set can be expressed as a linear combination of tensor-product interpolants over various intersections of the blocks that define it. Math Subject Classification: 41A05, 41A10, 65D05

Multivariate Polynomial Interpolation on Monotone Sets

New Approximations of the Total Variation and Filters in Image Processing

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

Multivariate polynomial interpolation: Aitken-Neville sets and generalized principal lattices

A suitably weakened definition of generalized principal lattices is shown to be equivalent to the recent definition of Aitken-Neville sets. The recent paper [CGS08] explores the relationship of Aitken-Neville sets, introduced in [SX], to generalized principal lattices, introduced in [CGS06]. Both are subsets X of F (with F equal to R or C) that are n-correct for some n in the sense that, with Π...