## A root-finding algorithm for cubics

HTML articles powered by AMS MathViewer

- 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

- Jane M. Hawkins,
*McMullen’s root-finding algorithm for cubic polynomials*, Proc. Amer. Math. Soc.**130**(2002), no. 9, 2583–2592. MR**1900865**, DOI 10.1090/S0002-9939-02-06659-5 - Curt McMullen,
*Families of rational maps and iterative root-finding algorithms*, Ann. of Math. (2)**125**(1987), no. 3, 467–493. MR**890160**, DOI 10.2307/1971408 - 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