Abstract
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.
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Rall, L.B. Early Automatic Differentiation: The Ch’in-Horner Algorithm. Reliable Comput 13, 303–308 (2007). https://doi.org/10.1007/s11155-006-9028-z
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DOI: https://doi.org/10.1007/s11155-006-9028-z