Polynomial Interpolation to Boundary Data on Triangles

Interpolation on Real Algebraic Curves to Polynomial Data

We discuss a polynomial interpolation problem where the data are of the form of a set of algebraic curves in R2 on each of which is prescribed a polynomial. The object is then to construct a global bivariate polynomial that agrees with the given polynomials when restricted to the corresponding curves. 2000 AMS subject classification: 41A10.

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 ...

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...

Note on Polynomial Interpolation to Analytic Functions.

last upper and lower molars. Chumashius balchi cannot, therefore, be regarded as occurring in the direct line of development leading upward to the Recent tarsier. In lower dental formula Chumashius exhibits a closer relationship to Omomys and Hemi4codon than to Anaptomorphus and Tetonius. The character of the lower posterior premolars in Uintanius suffice to remove this Bridger genus from any c...

Lectures on Multivariate Polynomial Interpolation