Alternate Derivation of Certain Formulae Related to Divided Differences.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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Alternate derivations are given of the usual formula for the divided difference as a linear combination of ordinates, Newtons divided-difference interpolation formula, the recursive relation underlying Aitkens linear interpolation process, the de Boor-Mansfield recurrence relation for B-splines, and Marsdens identity. These unconcentional derivations stem from i Kowalewskis 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 authors opinion, they provide a simpler and more natural development of these topics than the derivations customarily given. Author
- Theoretical Mathematics