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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.
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Cited by
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Metadata
- Authors
- Ypma, T. J.
- Venue
- SIAM Review
- Published
- 1995-12
- Volume
- 37
- Issue
- 4
- Pages
- 531-551
- ISSN
- 0036-1445 (ISSN-L)
- 1095-7200
- OpenAlex
- W2011777324
- Cited by
- 936
- References
- 0
- FWCI
- 14.81
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Historical Development of the Newton–Raphson Method. https://app.cochat.ai/papers/10.1137/1037125
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- Ypma, T. J. (1995). Historical Development of the Newton–Raphson Method. SIAM Review. https://doi.org/10.1137/1037125
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
