Newton法による近似解列の収束性とその初等的な新証明

Material type: 文書・図像類

Author: 那須, 信宏ほか

Publisher: 愛知工業大学

Publication date: 2002-03-31

Material Format: Digital

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Note (General)：: As the method of finding the approximate solutions of nonlinear equation, the Newton or the secant method is well known. But, the convergence of the a...

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Material Type: 文書・図像類
Title: Newton法による近似解列の収束性とその初等的な新証明
Author/Editor: 那須, 信宏
樋口, 功
Author Heading: 那須, 信宏
樋口, 功
Publication, Distribution, etc.: 愛知工業大学
Publication Date: 2002-03-31
Publication Date (W3CDTF): 2002-03-31
Alternative Title: Convergence of Sequences of Approximate Solutions by Newton Method and its Elementary New Proof
Periodical title: 愛知工業大学研究報告. A, 基礎教育センター論文集 = Bulletin of Aichi Institute of Technology. Part A
No. or year of volume/issue: 37
Volume: 37
Pages: 25-32
ISSN (Periodical Title): ISSN : 0387-0804
Text Language Code: jpn
Target Audience: 一般
Note (General): As the method of finding the approximate solutions of nonlinear equation, the Newton or the secant method is well known. But, the convergence of the approximate sequence {x_n} is not necessarily assured, Indeed, in many cases, the sequence {x_n} does not converge to the true solution. The classical proof of the convergence of the approximate sequence {x_n} is done with the help of the principle of contraction mapping under some additional conditions. The aim of this paper is to give an elementary new proof of the convergence of approximate sequence without using the principle of contraction mapping. We should like to remark that our new method is applicable to the proof of the more complicated case of the secant method.
identifier:http://repository.aitech.ac.jp/dspace/handle/11133/2023
Access Restrictions: 限定公開
Periodical Title (NCID): AA11564921
https://ci.nii.ac.jp/ncid/AA11564921
Data Provider (Database): 国立情報学研究所 : 学術機関リポジトリデータベース（IRDB）（機関リポジトリ）
https://irdb.nii.ac.jp
Original Data Provider (Database): 愛知工業大学 : 愛知工業大学学術情報リポジトリ