Early Automatic Differentiation: The Ch’in-Horner Algorithm

Autor:	Louis B. Rall
Rok vydání:	2006
Předmět:	Computational Mathematics symbols.namesake Polynomial Automatic differentiation Applied Mathematics Polynomial method Taylor series symbols Code generation Taylor coefficients Algorithm Software Mathematics
Zdroj:	Reliable Computing. 13:303-308
ISSN:	1573-1340 1385-3139
DOI:	10.1007/s11155-006-9028-z
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::4ecd38cac18ec976b1d0d62947d38da8 https://doi.org/10.1007/s11155-006-9028-z Zobrazit plný text záznamu Full text from SpringerLink