A root-finding algorithm for cubics
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- by Sam Northshield PDF
- Proc. Amer. Math. Soc. 141 (2013), 645-649 Request permission
Abstract:
Newton’s method applied to a quadratic polynomial converges rapidly to a root for almost all starting points and almost all coefficients. This can be understood in terms of an associative binary operation arising from $2\times 2$ matrices. Here we develop an analogous theory based on $3\times 3$ matrices which yields a two-variable generally convergent algorithm for cubics.References
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- Sam Northshield, On two types of exotic addition, Aequationes Math. 77 (2009), no. 1-2, 1–23. MR 2495716, DOI 10.1007/s00010-008-2952-8
Additional Information
- Sam Northshield
- Affiliation: Department of Mathematics, State University of New York, Plattsburgh, New York 12901
- Email: northssw@plattsburgh.edu
- Received by editor(s): June 1, 2010
- Received by editor(s) in revised form: June 22, 2011
- Published electronically: May 24, 2012
- Communicated by: Sergei K. Suslov
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 645-649
- MSC (2010): Primary 65H04; Secondary 26C10, 30D05, 37F10
- DOI: https://doi.org/10.1090/S0002-9939-2012-11324-3
- MathSciNet review: 2996969