Note on Polynomial Interpolation

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...

A note on cubic polynomial interpolation

“The NURBS Book” [L. Piegl, W. Tiller, The NURBS Book, second edn, Springer, 1997] is very popular in the fields of computer aided geometric design (CAGD) and geometric modeling. In Section 9.5.2 of the book, the well-known problem of the local cubic spline approximation is discussed. The key in local cubic spline approximation is cubic polynomial interpolation. In this short paper, we present ...

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...

Lectures on Multivariate Polynomial Interpolation