Abstract
An exploratory discussion of an ancient Chinese algorithm, the Ying Buzu Shu, in about 2 nd 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.
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Contributed by HE Ji-huan, Original Member of Editorial Committee, AMM
Foundation item: LNM, Institute of Mechanics, Chinese Academy of Sciences
Biography: HE Ji-huan (1965-)
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Ji-huan, H. Ancient chinese algorithm: The Ying Buzu Shu (method of surplus and deficiency) vs Newton iteration method. Appl Math Mech 23, 1407–1412 (2002). https://doi.org/10.1007/BF02438379
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DOI: https://doi.org/10.1007/BF02438379