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

HE Ji-huan

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Article Navigation > Applied Mathematics and Mechanics > 2002 > 23(12): 1255-1260

HE Ji-huan. Ancient Chinese Algorithm:The Ying Buzu Shu(Method of Surplus and Deficiency)vs Newton Iteration Method[J]. Applied Mathematics and Mechanics, 2002, 23(12): 1255-1260.

Citation:

HE Ji-huan. Ancient Chinese Algorithm:The Ying Buzu Shu(Method of Surplus and Deficiency)vs Newton Iteration Method[J]. Applied Mathematics and Mechanics, 2002, 23(12): 1255-1260.

Citation:

HE Ji-huan. Ancient Chinese Algorithm:The Ying Buzu Shu(Method of Surplus and Deficiency)vs Newton Iteration Method[J]. Applied Mathematics and Mechanics, 2002, 23(12): 1255-1260.

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

HE Ji-huan^1,2,3

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

Received Date: 2001-07-19
Rev Recd Date: 2002-04-01
Publish Date: 2002-12-15

Abstract

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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References(12)

References

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