一种古代的中国算法:盈不足术与牛顿迭代算法的比较

基金项目: 中国科学院院力学研究所非线性力学国家重点实验室资助项目

Ancient Chinese Algorithm:The Ying Buzu Shu(Method of Surplus and Deficiency)vs Newton Iteration Method

1.
LNM, Institute of Mechanics, Chinese Academy of Sciences, P R China;
2.
College of Science, Shanghai Donghua University, Shanghai 200051, P R China;
3.
Shanghai Institute of Applied Mathematics and Mechancis, Shanghai University, Shanghai 200072, P R China

摘要: 详细讨论了大约在公元前二世纪广泛流行的一种中国算法,这种算法在西方被称作为双假设法。强调指出双假设法是中国算法的一种译版。首次给出了中国算法与牛顿迭代算法之间的联系,如果引入了导数的概念,中国算法可以非常方便地转化为牛顿迭代算法。提出了一种改进的中国算法,并给出中国算法在非线性振动方程中的应用。
- 中国古代数学 /
- 九章算术 /
- 牛顿迭代算法 /
- Duffing方程
Abstract: An exploratory discussion of an ancient Chinese algorithm, the Ying Buzu Shu, in about 2nd century BC, known as the rule of double false position in the West is given. In addition to pointing out that the rule of double false position is actually a translation version of the ancient Chinese algorithm, a comparison with well-known Newton iteration method is also made. If derivative is introduced, the ancient Chinese algorithm reduces to the Newton method. A modification of the ancient Chinese algorithm is also proposed, and some of applications to nonlinear oscillators are illustrated.
- ancient Chinese mathematics /
- Jiuzhang Suanshu (Nine Chapters) /
- Newton iteration method /
- Duffing equation

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