Title
Historical development of the Newton-Raphson method
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.
Year
DOI
Venue
1995
10.1137/1037125
SIAM Review
Keywords
Field
DocType
nonlinear equations,iteration,Newton-Raphson method,Isaac Newton,Joseph Raphson,Thomas Simpson
Simpson's rule,Mathematical optimization,Nonlinear system,System of linear equations,Iterative and incremental development,Algebraic equation,Extant taxon,Kepler orbit,Mathematics,Newton's method
Journal
Volume
Issue
ISSN
37
4
0036-1445
Citations 
PageRank 
References 
117
7.70
0
Authors
1
Search Limit
100117
Name
Order
Citations
PageRank
Tjalling J. Ypma11199.96