Alternate Derivation of Certain Formulae Related to Divided Differences.
Abstract
Alternate derivations are given of the usual formula for the divided difference as a linear combination of ordinates, Newton's divided-difference interpolation formula, the recursive relation underlying Aitken's linear interpolation process, the de Boor-Mansfield recurrence relation for B-splines, and Marsden's identity. These unconcentional derivations stem from (i) Kowalewski's suggestion that the divided difference of order n be defined as the coefficient of (x sup n) in the Waring-Lagrange interpolating polynomial, rather than in the conventional manner, and (ii) a general formula for divided differences of a certain class of functions of two variables. In the author's opinion, they provide a simpler and more natural development of these topics than the derivations customarily given. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1972
- Accession Number
- AD0748761
Entities
People
- Thomas N.E. Greville
Organizations
- University of Wisconsin–Madison