A root-finding algorithm for cubics

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Authors
Northshield, Sam
Issue Date
2013
Type
Article
Language
en_US
Keywords
Newton's method , iterative algorithm , generally convergent
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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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This article has been published in Proceedings of the American Mathematical Society: https://doi.org/10.1090/S0002-9939-2012-11324-3
Citation
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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Proceedings of the American Mathematical Society
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