Document Type

Article

Publication Date

2013

Publication Title

Proceedings of the American Mathematical Society

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 × 2 matrices. Here we develop an analogous theory based on 3 × 3 matrices which yields a two-variable generally convergent algorithm for cubics.

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