| ANCIENT CHINESE ALGORITHM: THE YING BUZU SHU (METHOD OF SURPLUS AND DEFICIENCY)VS NEWTON ITERATION METHOD |
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| 引用本文： | 何吉欢. ANCIENT CHINESE ALGORITHM: THE YING BUZU SHU (METHOD OF SURPLUS AND DEFICIENCY)VS NEWTON ITERATION METHOD[J]. 应用数学和力学(英文版), 2002, 23(12): 1407-1412. DOI: 10.1007/BF02438379 |
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| 作者姓名： | 何吉欢 |
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| 作者单位： | LNM，Institute of Mechanics，Chinese Academy of Sciences P R China，College of Science，Shanghai Donghua University，Shanghai 200051，P R China，Shanghai Institute of Applied Mathematics and Mechanics，Shanghai University，Shanghai 200072，P R China |
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| 基金项目： | LNMInstituteofMechanicschineseAcademyofSciences |
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| 摘 要： | 1 ＡｎＩｎｔｒｏｄｕｃｔｉｏｎｔｈｅＪｉｕｚｈａｎｇＳｕａｎｓｈｕ (九章算术 )ＥｓｓｅｎｔｉａｌｌｙｎｏｔｈｉｎｇｏｆａｐｒｉｍａｒｙｎａｔｕｒｅｈａｓｃｏｍｅｄｏｗｎｔｏＷｅｓｔｃｏｎｃｅｒｎｉｎｇａｎｃｉｅｎｔＣｈｉｎｅｓｅｍａｔｈｅｍａｔｉｃｓ,ｌｉｔｔｌｅｈａｓｂｅｅｎｄｉｓｃｕｓｓｅｄｏｎａｎｃｉｅｎｔＣｈｉｎｅｓｅｍａｔｈｅｍａｔｉｃｓｉｎｓｏｍｅｏｆｔｈｅｍｏｓｔｆａｍｏｕｓｍｏｎｏｇｒａｐｈｓｏｎｈｉｓｔｏｒｙｏｆｍａｔｈｅｍａｔｉｃｓ[1- 3].Ｓｏｔｈｅｐｒｅｓｅｎｔａｕｔｈｏｒ…
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| 收稿时间： | 2001-07-19 |
Ancient chinese algorithm: The Ying Buzu Shu (method of surplus and deficiency) vs Newton iteration method |
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| He Ji-huan Professor, Doctor. Ancient chinese algorithm: The Ying Buzu Shu (method of surplus and deficiency) vs Newton iteration method[J]. Applied Mathematics and Mechanics(English Edition), 2002, 23(12): 1407-1412. DOI: 10.1007/BF02438379 |
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| Authors: | He Ji-huan Professor Doctor |
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| Affiliation: | LNM, Institute of Mechanics, Clinese Academy of Sciences, P R China;College of Science, Shanghai Donghua University, Shanghai 200051, P R China;Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University,Shanghai 200072, P R China |
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| 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. |
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| Keywords: | ancient Chinese mathematics Jiuzhang Suanshu(Nine Chapters) Newton iteration method Duffing equation |
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