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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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