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A Simple Method for Finding the Zeros of Polynomials, Based on d’Alembert’s Lemma

机译：基于d'alembert引理的一种求多项式零点的简单方法

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摘要

This report describes a method for approximating the roots of a poly¬nomial equation on an electronic digital computer. The method is based on d'Alembert's Lemma of algebra, which states that the absolute value of a polynomial assumes a minimum if and only if it is zero. Comparison of the method with other techniques for solving polynomial equations leads to the conclusion that, in addition to simplicity, the new method offers timing and accuracy quite comparable to those of other methods coded with the same precision and sophistication.

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作者
Zane C. Motteler;
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年度 1965
页码 1-29
总页数 29
原文格式 PDF
正文语种 eng
中图分类工业技术;
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1. Computer methodologies for comparison of computational efficiency of simultaneous methods for finding polynomial zeros [J] . Journal of Computational and Applied Mathematics . 2020,第期

机译：用于比较多项式零的同时方法的计算效率的计算机方法
2. A SIMPLE ITERATIVE PROCEDURE FOR FINDING ALL ZEROS OF A POLYNOMIAL WITHOUT REPEATED EVALUATION [J] . 郑士明高等学校计算数学学报：英文版 . 1996,第002期

机译：一种简单的迭代过程，用于在没有重复评估的情况下找到多项式的所有零
3. On the guaranteed convergence of new two-point root-finding methods for polynomial zeros [J] . Miodrag S. Petkovi?, Lidija Z. Ran?i? Numerical algorithms . 2014,第1期

机译：关于多项式零点的新两点求根方法的保证收敛性
4. Some Accurate Methods for Finding Simple Roots of Polynomials in Floating Point Arithmetic [C] . Du, Peibing, Cheng, Lizhi, Jiang, Hao, ICCIS 2012;International conference on computational and information sciences . 2012

机译：浮点算法中多项式求根的一些精确方法
5. A solution method for zero dimensional polynomial equation systems and a pose-free framework for the robust solution of the structure from motion problem. [D] . Zhang, Ji. 2009

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6. Numerical Evaluation and Comparison of Kalantari's Zero Bounds for Complex Polynomials [O] . Matthias Dehmer, Yury Robertovich Tsoy 2010

机译：复多项式的Kalantari零界的数值评估和比较
7. Jacobi-free and complex-free method for finding simultaneously all zeros of polynomials having only real zeros [O] . Wu Xingyuan, Shao Rong, Zhu Yiran 2003

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8. Application of the Nelder-Mead Simplexnto Finding the Zeros of Polynomials [R] . Zane C. Motteler 1969

机译：Nelder-mead simplexnto在多项式零点中的应用

A Simple Method for Finding the Zeros of Polynomials, Based on d’Alembert’s Lemma

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