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Computational Divided Differencing and Divided-Difference Arithmetics (2000)
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| Citations: | 3 - 0 self |
BibTeX
@MISC{Reps00computationaldivided,
author = {Thomas W. Reps and Louis B. Rall},
title = {Computational Divided Differencing and Divided-Difference Arithmetics},
year = {2000}
}
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Abstract
Tools for computational differentiation transform a program that computes a numerical function F (x) into a related program that computes F 0 (x) (the derivative of F ). This paper describes how techniques similar to those used in computational-differentiation tools can be used to implement other program transformations -- in particular, a variety of transformations for computational divided differencing . The specific technical contributions of the paper are as follows: It presents a program transformation that, given a numerical function F (x) de ned by a program, creates a program that computes F [x0 ; x1 ], the first divided difference of F(x), where F [x0 ; x1 ] def = F (x 0 ) F (x 1 ) x 0 x 1 if x0 6= x1 d dz F (z); evaluated at z = x0 if x0 = x1 It shows how computational first divided differencing generalizes computational differentiation. It presents a second program transformation that permits the creation of higher-order divided differences of a numerical function de ...
Keyphrases
numerical function divided-difference arithmetic computational divided differencing program transformation computational differentiation related program computational-differentiation tool generalizes computational differentiation specific technical contribution x1 dz second program transformation higher-order divided difference x1 def
