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A root-finding algorithm for cubics

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Newton's method
 iterative algorithm
 generally convergent
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2013
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SUNY Plattsburgh Mathematics Faculty Work
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http://hdl.handle.net/20.500.12648/1113
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 x 2 matrices. Here we develop an analogous theory based on 3 x 3 matrices which yields a two-variable generally convergent algorithm for cubics.
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Northshield, S. (2013). A root-finding algorithm for cubics. Proceedings of the American Mathematical Society, 141(2). http://doi.org/10.1090/S0002-9939-2012-11324-3
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This article has been published in Proceedings of the American Mathematical Society: https://doi.org/10.1090/S0002-9939-2012-11324-3
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