斐波那契-曼德勃洛特多项式和矩阵

Eunice Y. S. Chan, Robert M Corless
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引用次数: 4

摘要

我们探索了一个类似于Mandelbrot多项式的多项式族,称为fibonaci -Mandelbrot多项式,由q0(z) = 0, q1(z) = 1和qn(z) = zqn−1qn−2 + 1定义。我们用两种方法计算斐波那契-曼德布洛特多项式的根。一种方法使用递归构造的矩阵,其中元素为0、1或−1,其特征值是qn(z)的根。另一种方法采用专用同伦延拓方法,其中初始条件为0的微分方程[equation]的解,以及qn−1和qn−2的根,也是fibonaci - mandelbrot多项式的根。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Fibonacci-mandelbrot polynomials and matrices
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.
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