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Title :村瀬義益の3次方程式の逐次近似法の拡張定理とニュートン法の拡張定理の関連について
Title alternative :On Relations Between Enhancing Theorems of the Methods of the Murase's Successive Approximations of a Cubic Equation and the Enhancing Theorems of the Newton's Method
Authors :堀口, 俊二
Publisher :新潟産業大学附属研究所
Issue Date :Nov-2009
Journal Title :新潟産業大学経済学部紀要
Volume :37
Start Page :57
End Page :94
ISSN :1341-1551
Abstract :村瀬義益(新潟佐渡・東京・千葉)は『算法勿憚改』(1673,1674新刊,1681開板『算学淵底記』)を著した.村瀬はこの書において,ある種の3次方程式を3通りの逐次近似法で解くという,世界数学史上でも稀有な計算を成し遂げた.§1は『算法勿憚改』にある3次方程式の逐次近似法の説明である.§2はこれらの拡張定理Iである.さらに§3,4,5 は拡張定理II,III,IVである.§5はこの論文の主テーマである.それは村瀬の拡張漸化式とニュートンの拡張漸化式の関連を与える.定理31は主定理である.§6はパソコンを使い,村瀬の拡張漸化式,ニュートンの漸化式および村瀬・ニュートンの拡張漸化式の数値計算を行う.§7においてこれらを考察・比較する.§8は村瀬の逐次近似法の考え方とその歴史的考察である.§9はまとめである.§10は本稿の内容から,コンピュータ実習および数学教育の教材を与える.§11は研究課題である.
Yoshimasu Murase(Sado Niigata・Tokyo・Chiba) wrote the Sanpo Hutudankai(算法勿憚改)(1673, 1674) or Sangaku-Yenteiki(算学淵底記)(1681). Murase performed rare calculations in the world mathematics history to solve a certain cubic equation by methods of successive approximation in this book. §1 is an explanation of methods of successive approximations of a cubic equation in 算法勿憚改. §2 gives enhancing theorems I of them. Furthermore,§3, 4, 5 gives enhancing theorems II , III,IV respectively. §5 is a main theme of this paper. It give relations between the Murase's enhanced recurrence formulas and Newton's enhanced recurrence formulas(methods), and Theorem 31 is the main theorem. §6 calculate the Murase's enhanced recurrence formulas, Newton's recurrence formula and Murase・Newton's enhanced recurrence formula by a personal computer. §7 give the comparisons and considerations of them. §8 state the idea of the approximation methods of Murase and the historical considerations of them. §9 is settling. §10 give the teaching materials of the computer practices and the mathematics educations from the contents of this paper. §11 is research challenges.
Type Local :Departmental Bulletin Paper
Language :jpn
URI :http://hdl.handle.net/10623/20347
Appears in Collections:01 新潟産業大学経済学部紀要

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