On hermite interpolation by Cauchy-Vandermonde systems

The Lagrange formula, the adjoint and the inverse of a Cauchy-Vandermonde matrix

authored by

G. Mühlbach

Abstract

For a given Cauchy-Vandermonde system and for given multiple nodes a Lagrange-type formula for the interpolant is derived, interpolating a given function in the sense of Hermite. We give explicit analytic representations of the basic functions in terms of the nodes and prescribed poles. They are used to derive formulas for the entries of the adjoint of the confluent Cauchy-Vandermonde matrix corresponding to the interpolation problem thus providing an explicit representation of its inverse.

Organisation(s)

Institute of Applied Mathematics

Type

Article

Journal

Journal of Computational and Applied Mathematics

Volume

67

Pages

147-159

No. of pages

13

ISSN

0377-0427

Publication date

20.02.1996

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Computational Mathematics, Applied Mathematics

Electronic version(s)

https://doi.org/10.1016/0377-0427(94)00116-2 (Access: Open)