Accession Number : AD0748761

Title :   Alternate Derivation of Certain Formulae Related to Divided Differences.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Greville,T. N. E.

Report Date : AUG 1972

Pagination or Media Count : 17

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)

Descriptors :   (*NUMERICAL ANALYSIS, POLYNOMIALS), INTERPOLATION, APPROXIMATION(MATHEMATICS), ALGEBRA

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE