On multivariate polynomial interpolation |
| |
| Authors: | Carl de Boor Amos Ron |
| |
| Affiliation: | 1. Center for Mathematical Sciences, University of Wisconsin-Madison, 610 Walnut Street, 53705, Madison Wisconsin, USA
|
| |
| Abstract: | ![]()
We provide a map which associates each finite set  in complexs-space with a polynomial space  from which interpolation to arbitrary data given at the points in is possible and uniquely so. Among all polynomial spacesQ from which interpolation at is uniquely possible, our is of smallest degree. It is alsoD- and scale-invariant. Our map is monotone, thus providing a Newton form for the resulting interpolant. Our map is also continuous within reason, allowing us to interpret certain cases of coalescence as Hermite interpolation. In fact, our map can be extended to the case where, with eachgq , there is associated a polynomial space P, and, for given smoothf, a polynomialqQ is sought for which
|
|
