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Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (12): 1407-1412.

• 论文 • 上一篇    下一篇

ANCIENT CHINESE ALGORITHM: THE YING BUZU SHU (METHOD OF SURPLUS AND DEFICIENCY) VS NEWTON ITERATION METHOD

何吉欢1,2,3   

  1. 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 Mechanics, Shanghai University, Shanghai 200072, P. R. China
  • 收稿日期:2001-07-19 修回日期:2002-04-01 出版日期:2002-12-18 发布日期:2002-12-18
  • 基金资助:
    LNM,Institute of Mechanics,Chinese Academy of Sciences

ANCIENT CHINESE ALGORITHM: THE YING BUZU SHU (METHOD OF SURPLUS AND DEFICIENCY) VS NEWTON ITERATION METHOD

HE Ji-huan1,2,3   

  1. 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 Mechanics, Shanghai University, Shanghai 200072, P. R. China
  • Received:2001-07-19 Revised:2002-04-01 Online:2002-12-18 Published:2002-12-18
  • Supported by:
    LNM,Institute of Mechanics,Chinese Academy of Sciences

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摘要： 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.

关键词: ancient Chinese mathematics, Jiuzhang Suanshu(Nine Chapters), Newton iteration method, Duffing equation

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.

Key words: ancient Chinese mathematics, Jiuzhang Suanshu(Nine Chapters), Newton iteration method, Duffing equation

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