Document Type

Article

Publication Date

1995

Keywords

Nonlinear equations, Iteration, Isaac Newton, Joseph Raphson, Thomas Simpson

Abstract

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.

Publication Title

SIAM Review

Volume

37

Issue

4

First Page

531

Last Page

551

Required Publisher's Statement

Copyright 1995 Society for Industrial and Applied Mathematics

Courtesy of JSTOR

Stable URL: http://www.jstor.org/stable/2132904

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

Genre/Form

articles

Type

Text

Rights

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.

Language

English

Format

application/pdf

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Mathematics Commons

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