Nonlinear equations, Iteration, Isaac Newton, Joseph Raphson, Thomas Simpson
This expository paper traces the development of the Newton-Raphson method for solving nonlinear algebraic equations through the extant notes, letters, and publications of Isaac Newton, Joseph Raphson, and Thomas Simpson. It is shown how Newton's formulation differed from the iterative process of Raphson, and that Simpson was the first to give a general formulation, in terms of fluxional calculus, applicable to nonpolynomial equations. Simpson's extension of the method to systems of equations is exhibited.
Required Publisher's Statement
Copyright 1995 Society for Industrial and Applied Mathematics
Courtesy of JSTOR
Stable URL: http://www.jstor.org/stable/2132904
Ypma, Tjalling, "Historical Development of the Newton-Raphson Method" (1995). Mathematics. 93.
Subjects - Topical (LCSH)
Calculus--History; Newton-Raphson method; Nonlinear theories
Subjects - Names (LCNAF)
Newton, Isaac, 1642-1727; Raphson, Joseph, -1715 or 1716; Simpson, Thomas, 1710-1761
Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.