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πとeの連分数展開とその数値計算法
https://otsuma.repo.nii.ac.jp/records/758
https://otsuma.repo.nii.ac.jp/records/758a17fe79b-16ec-4bf7-b26b-4d6deb7500ba
名前 / ファイル | ライセンス | アクション |
---|---|---|
KJ00004766727.pdf (232.6 kB)
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Item type | 紀要論文(ELS) / Departmental Bulletin Paper(1) | |||||
---|---|---|---|---|---|---|
公開日 | 2006-01-01 | |||||
タイトル | ||||||
タイトル | πとeの連分数展開とその数値計算法 | |||||
タイトル | ||||||
言語 | en | |||||
タイトル | Expansions of π and e into Continued Fractions and their Numerical Evaluation | |||||
言語 | ||||||
言語 | jpn | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | ブランカーの公式 | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | 連分数展開 | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | 円周率π | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | 自然対数の底e | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | 数値計算 | |||||
キーワード | ||||||
主題Scheme | Other | |||||
主題 | 桁あふれ | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | Brounker's formula | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | expansion into continued fraction | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | the number π | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | the number e, the base of natural logarithm | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | numerical evaluation | |||||
キーワード | ||||||
言語 | en | |||||
主題Scheme | Other | |||||
主題 | overflow | |||||
資源タイプ | ||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||
資源タイプ | departmental bulletin paper | |||||
ページ属性 | ||||||
内容記述タイプ | Other | |||||
内容記述 | P(論文) | |||||
論文名よみ | ||||||
その他のタイトル | π ト e ノ レンブンスウ テンカイ ト ソノ スウチ ケイサンホウ | |||||
著者名(日) |
野崎, 昭弘
× 野崎, 昭弘 |
|||||
著者名よみ | ||||||
識別子 | 2057 | |||||
姓名 | ノザキ, アキヒロ | |||||
著者名(英) | ||||||
識別子 | 2058 | |||||
姓名 | Nozaki, Akihiro | |||||
言語 | en | |||||
著者所属(日) | ||||||
大妻女子大学社会情報学部 | ||||||
著者所属(英) | ||||||
en | ||||||
School of Social Information Studies, Otsuma Women's University | ||||||
抄録(日) | ||||||
内容記述タイプ | Other | |||||
内容記述 | 円周率πを表すいわゆるブランカーの公式の初等的な導き方を示し,その打切り誤差が,π/4の逆数をグレゴリー級数で表したときの打切り誤差と正確に一致することを示した。またその導き方を応用して,自然対数の底eの収束の速い連分数展開を与えた。さいごにそれらの無限連分数の数値計算法を検討して,これまでに知られている直接的な計算法をブランカーの公式に当てはめるとすぐ桁あふれが起こってしまう(最初の10項しか計算できない)こと,また本論文で提案される計算法によれば,桁あふれを大幅に抑えられる(4百万項計算できる)ことを示した。 | |||||
抄録(英) | ||||||
内容記述タイプ | Other | |||||
内容記述 | In this paper, we have shown an elementary method to derive Brounker's Formula, an expansion of the number π into continued fraction, and proved that its truncation error is identical with that of the evaluation of the reciprocal of π/4 by Gregory's series. By the same method, we obtained an infinite continued fraction which converges very rapidly to the value of e, the base of natural logarithm. We finally examined numerical evaluation of infinite continued fractions, and have shown that Brounker's Formula is practically intractable by the ordinary straight-forward method, because overflow occurs in the very early stage of computation, while its evaluation can be continued much further without overflow by the method presented in this paper. | |||||
雑誌書誌ID | ||||||
収録物識別子タイプ | NCID | |||||
収録物識別子 | AN10407566 | |||||
書誌情報 |
大妻女子大学紀要. 社会情報系, 社会情報学研究 en : Otsuma journal of social information studies 巻 15, p. 251-255, 発行日 2006 |