秦九韶算法与牛顿迭代法的比较

Qin Jiushao Algorithm and Newton s Iterative Method

研究“秦九韶算法”在解方程过程中各步骤的意义,对比牛顿迭代法发现两者具有相似之处,前者是世界上首次提出任意高次方程的数值解法,具有机械化、整齐化等优点,其运算方法部分与现代综合除法相同;后者虽提出较晚但其适用范围更为广阔,且计算简单、收敛速度较快.

This paper studies the Qin Jiushao Algorithm for solving polynomial equations of higher order,compares it with the Newton Iteration Method,and presents their similarities and differences.The former,the first in the world,is to find a numerical solution for any higher-order polynomial equation,which has the advantages of mechanization and neatness.Some parts of its calculation is the same as the division method nowadays.The latter has wider applications,simpler iteration formula and faster convergence rate.