代数代数基本定理的可视化构造性证明及多项式根估计的并行算法
A Visualizable, Constructive Proof of the Fundamental Theorem of Algebra, and a Parallel Polynomial Root Estimation Algorithm
摘要：
本文给出了代数代数基本定理的另一种证明方法，它有几个明显的优点。证明是基于简单的想法，包括连续性和差异。可视化软件演示可以用来传达证明的要点。一个严格的证明版本可以只使用单变量微积分和复数的基本性质，但技术细节有点涉及。为了便于读者直观地掌握证明，我们首先提出论证的要点，这些要点可以通过计算机实验来说明。接下来，我们使用单变量微积分来填充一些细节。最后给出了一个并行求解2n个微分方程的n次多项式的全部根的数值方法。
英文摘要：
This paper presents an alternative proof of the Fundamental Theorem of Algebra that has several distinct advantages. The proof is based on simple ideas involving continuity and differentiation. Visual software demonstrations can be used to convey the gist of the proof. A rigorous version of the proof can be developed using only single-variable calculus and basic properties of complex numbers, but the technical details are somewhat involved. In order to facilitate the reader's intuitive grasp of the proof, we first present the main points of the argument, which can be illustrated by computer experiments. Next we fill in some of the details, using single-variable calculus. Finally, we give a numerical procedure for finding all roots of an n'th degree polynomial by solving 2n differential equations in parallel.
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。
