基于Dickson基表示的回文矩阵多项式的Ehrlich-Aberth方法

Diverging orbits for the Ehrlich-Aberth and the Weierstrass root finders

We show that the higher dimensional Weierstrass and Ehrlich-Aberth methods for finding roots of polynomials have infinite orbits that diverge to infinity. This is possible for the Jacobi update scheme (all coordinates are updated in parallel) as well as Gauss-Seidel (any coordinate update is used for all subsequent coordinates).

通过Ehrlich-Aberth方法求解多项式特征值问题

Solving polynomial eigenvalue problems by means of the Ehrlich-Aberth method

本文采用Ehrlich-Aberth迭代，将多项式特征值问题视为标量多项式det P(x)的求根问题，讨论了起始近似选择、牛顿修正计算、停机准则及无穷远特征值处理，实现了比基于QZ算法更精确的特征值近似，并针对特殊结构多项式（如回文、Hamiltonian、辛等）提出了适应Ehrlich-Aberth迭代的通用方法。

Finding polynomial roots by dynamical systems -- a case study

We investigate two well known dynamical systems that are designed to find roots of univariate polynomials by iteration: the methods known by Newton and by Ehrlich-Aberth. Both are known to have found all roots of high degree polynomials with good complexity. Our goal is to determine in which cases which of the two algorithms is more efficient. We come to the conclusion that Newton is faster when the polynomials are given by recursion so they can be evaluated in logarithmic time with respect to the degree, or when all the roots are all near the boundary of their convex hull. Conversely, Ehrlich…

定位矩阵多项式的特征值

Locating the eigenvalues of matrix polynomials

将多项式根定位的已知结果推广到矩阵多项式，用于为同时迭代法（如Ehrlich-Aberth方法）提供有效的初始近似，并通过数值实验展示计算优势。

曼德勃罗多项式根的数值计算：一项实验分析

Numerical computation of the roots of Mandelbrot polynomials: an experimental analysis

本文提出一种基于Ehrlich-Aberth迭代与快速多极方法的算法，高效计算曼德勃罗多项式的根，实验验证了其O(n log n)复杂度和O(log n)迭代次数，并推导出实根渐近表达式。