• A root-finding algorithm for cubics

      Northshield, Sam (Proceedings of the American Mathematical Society, 2013)
      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.