Historical development of the Newton-Raphson method

被引:598
作者
Ypma, TJ
机构
[1] Western Washington Univ, Bellingham, WA
关键词
nonlinear equations; iteration; Newton-Raphson method; Isaac Newton; Joseph Raphson; Thomas Simpson;
D O I
10.1137/1037125
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:531 / 551
页数:21
相关论文
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