An algorithmic approach to Hermite-Birkhoff-interpolation

verfasst von

G. Mühlbach

Abstract

This paper deals with an algorithmic approach to the Hermite-Birkhoff-(HB)interpolation problem. More precisely, we will show that Newton's classical formula for interpolation by algebraic polynomials naturally extends to HB-interpolation. Hence almost all reasons which make Newton's method superior to just solving the system of linear equations associated with the interpolation problem may be repeated. Let us emphasize just two: Newton's formula being a biorthogonal expansion has a well known permanence property when the system of interpolation conditions grows. From Newton's formula by an elementary argument due to Cauchy an important representation of the interpolation error can be derived. All of the above extends to HB-interpolation with respect to canonical complete Čebyšev-systems and naturally associated differential operators [7]. A numerical example is given.

Organisationseinheit(en)

Institut für Angewandte Mathematik

Typ

Artikel

Journal

Numerische Mathematik

Band

37

Seiten

339-347

Anzahl der Seiten

9

ISSN

0029-599X

Publikationsdatum

10.1981

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Computational Mathematics, Angewandte Mathematik

Elektronische Version(en)

https://doi.org/10.1007/BF01400313 (Zugang: Geschlossen)