高阶根精炼器
Higher-order root distillers
AI总结：
本文提出高阶根精炼器，通过递归映射实现高收敛阶m的单调步骤函数，用于精确分离和计算区间内函数的真实根。
摘要：
高阶收敛阶m（如m=2^10或m=2^20）的递归映射诱导出某些单调步骤函数，从中可过滤出用于全局分离和计算给定区间[a,b]上函数真实根所需的信息。此过程称为根精炼器。合适的根精炼器具有强大的预条件效应，可在整个区间内精确计算高次多项式根。以高次不精确切比雪夫多项式为模型，利用Mathematica系统给出数值实例，详细说明我们的精炼器算法。
英文摘要：
Recursive maps of high order of convergence $m$ (say $m=2^{10}$ or $m=2^{20}$) induce certain monotone step functions from which one can filter relevant information needed to globally separate and compute the real roots of a function on a given interval $[a,b]$. The process is here called a root distiller. A suitable root distiller has a powerful preconditioning effect enabling the computation, on the whole interval, of accurate roots of an high degree polynomial. Taking as model high-degree inexact Chebyshev polynomials and using the {\sl Mathematica} system, worked numerical examples are given detailing our distiller algorithm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
