An algorithmic approach to Hermite-Birkhoff-interpolation

authored by: 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.
Organisation(s): Institute of Applied Mathematics
Type: Article
Journal: Numerische Mathematik
Volume: 37
Pages: 339-347
No. of pages: 9
ISSN: 0029-599X
Publication date: 10.1981
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/BF01400313 (Access: Closed)