
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 divideddifference interpolation formula, the recursive relation underlying Aitken's linear interpolation process, the de BoorMansfield recurrence relation for Bsplines, 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 WaringLagrange 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