Eunice Y. S. Chan
Robert M. Corless
Abstract
We explore a family of polynomials similar to the Mandelbrot polynomials called the Fibonacci-Mandelbrot polynomials defined by q0(z) = 0, q1(z) = 1, and qn(z) = zqn−1qn−2 + 1. We compute the roots of the Fibonacci-Mandelbrot polynomials using two methods. One method uses a recursively constructed matrix, where elements are 0, 1, or −1, whose eigenvalues are the roots of qn(z). The other method uses a special-purpose homotopy continuation method, where the solution of the differential equation, [EQUATION], in which the initial condition are 0, and the roots of qn−1 and qn−2, are also the roots of the Fibonacci-Mandelbrot polynomials.
- Robert M. Corless & Nicolas Fillion. A graduate introduction to numerical methods. Springer, 2013. Google Scholar
Digital Library
- Robert M. Corless & Piers W. Lawrence. Mandelbrot polynomials and matrices. In preparation.Google Scholar
- Robert M. Corless et al. Bohemian Eigenvalues. In preparation.Google Scholar
- Fuzhen Zhang, ed. The Schur complement and its application. Vol. 4. Springer Science & Business media, 2006.Google Scholar
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