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Abstract: . We present a purely functional implementation of the computational differentiation tools --- the well known numeric (i.e., not symbolic) techniques which permit one to compute point-wise derivatives of functions defined by computer programs economically and exactly (with machine precision). We show how the use of lazy evaluation permits a transparent and elegant construction of the entire infinite tower of derivatives of higher order for any expressions present in the program. The formalism... (Update)
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...operations. These operations augmented by the derivation operator which yields the derivative, form a local differential algebra. In [2, 3] we have shown how to augment the typical scientific programs, by the derivation operator using a functional version of the...
.... to represent extrusions and other generalized sweeps, and we show how the usage of the algorithmic differentiation techniques (see [1, 2], and references therein, mainly [3] might simplify enormously the manipulation of tangents to trajectories, normals to surfaces,...
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Scientific Computation and Functional Programming - Karczmarczuk (1999) (Correct)
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3: Generating Power of Lazy Semantics - Karczmarczuk - 1997
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BibTeX entry: (Update)
Jerzy Karczmarczuk, Functional Differentiation of Computer Programs, Proceedings of the III ACM SIGPLAN International Conference on Functional Programming, Baltimore, (1998), pp. 195--203. http://citeseer.ist.psu.edu/karczmarczuk98functional.html More
@inproceedings{ karczmarczuk98functional,
author = "Jerzy Karczmarczuk",
title = "Functional Differentiation of Computer Programs",
booktitle = "International Conference on Functional Programming",
pages = "195-203",
year = "1998",
url = "citeseer.ist.psu.edu/karczmarczuk98functional.html" }
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Documents on the same site (http://users.info.unicaen.fr/~karczma/arpap/): More
Geometric Modelling in Functional Style - Karczmarczuk (1999) (Correct)
Scientific Computation and Functional Programming - Karczmarczuk (1999) (Correct)
Lazy Differential Algebra and its Applications - Karczmarczuk (1998) (Correct)
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