Early Automatic Differentiation: The Ch’in-Horner Algorithm

Early Automatic Differentiation: The Ch’in-Horner Algorithm A method for numerical solution of polynomial equations appeared in the 1247 a.d. book The Nine Sections of Mathematics, by Ch’in Kiu-shao. This procedure was rediscovered independently by W. G. Horner [1773–1827] at the beginning of the 19th century. Since their algorithm produces values of Taylor coefficients of polynomials, it can be viewed as an early example of automatic differentiation. For polynomials, their method is shown to be computationally equivalent to automatic generation of Taylor coefficients as introduced by R. E. Moore in 1962 for use on digital computers. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Early Automatic Differentiation: The Ch’in-Horner Algorithm

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2007 by Springer Science + Business Media B.V.
Subject
Mathematics; Numeric Computing; Mathematical Modeling and Industrial Mathematics; Approximations and Expansions; Computational Mathematics and Numerical Analysis
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1007/s11155-006-9028-z
Publisher site
See Article on Publisher Site

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