What is the Qin Jiushao program?
This article will explain in detail what the Qin Jiushao program is. The editor thinks it is very practical, so I share it for you as a reference. I hope you can get something after reading this article.
"positive and negative prescription", known as "Qin Jiushao procedure", occupied a leading position in the field of mathematics at that time. It was not until more than 500 years later, in 1819, that the British mathematician Horner put forward the "Horner method" which was the same as the principle of this achievement.
"positive and negative prescription" is also known as "Qin Jiushao procedure".
Positive and negative prescription is an ancient Chinese algorithm, which refers to a method of finding the numerical solution of univariate higher order equation in ancient China. This method was obtained by Qin Jiushao, a mathematician in the Southern Song Dynasty, who summarized and improved the "prescription" of "Shu Nine chapters", Liu Yi's "positive and negative prescription" and Jia Xian's "multiplication method".
"positive and negative prescription" is an algorithm to transform the evaluation problem of unary n-degree polynomials into n-degree polynomials. It greatly simplifies the calculation process, even in modern times, when using computers to solve the evaluation problem of polynomials, Qin Jiushao algorithm is still the best algorithm.
It is called Horner algorithm in the West and is named after Horner, a British mathematician.
Calculation method.
Generally speaking, the evaluation of unary polynomial of degree n needs to go through (n times 1) * n times multiplication and n times addition, while Qin Jiushao algorithm only needs n times multiplication and n times addition. In manual calculation, the operation process is greatly simplified at one time.
Conclusion: for a polynomial of degree n, do at most n times multiplication and n times addition.
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