确定代数方程根位置的快速无除算法

A Fast Fraction-Free Method to Determine the Zero-Location of Algebraic Equation

中文关键词:  Bezout矩阵  多项式余项序列  矩阵惯性  无平方

英文关键词:Bezout matrix  prs （polynomial remainder sequence）  matrix inertia  squarefree.

中文摘要:

      本文提供了一个确定整系数代数方程在指定区域内根的个数的快速无除算法,此算法的复杂性为O(n²),其中n为方程的次数.为了强凋算法的稳定性,本文均用精确的整数运算.其中多项式是无平方的、首一的.

英文摘要:

      In this paper, we present a fast and fraction-free procedure for determining the zero-location of an algebraic equation with integer coefficients in any rectangle area in complex plane, where the polymomial is squarefree and monic, and the coordinates of the vertices of the rectangle are integers. In order to address the stability problems, we use exact arithmetic only.