Approximate Zero-points of Real Univariate Polynomial with Large Error Terms

• Item type: Journal(1)
• 公開日: 2000-04-15
• タイトル: Approximate Zero-points of Real Univariate Polynomial with Large Error Terms
• タイトル / 言語: en
• タイトル: Approximate Zero-points of Real Univariate Polynomial with Large Error Terms
• 言語: eng
• キーワード / 主題Scheme: Other
• キーワード / 主題: 論文
• 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: journal article
• その他タイトル / その他のタイトル: 基礎理論
• 著者所属: Institute of Mathematics University of Tsukuba
• 著者所属: Institute of Mathematics University of Tsukuba
• 著者所属(英): en
• 著者所属(英): Institute of Mathematics, University of Tsukuba
• 著者所属(英): en
• 著者所属(英): Institute of Mathematics, University of Tsukuba
• 著者名: Akira, Terui; Tateaki, Sasaki
• 著者名(英): Akira, Terui; Tateaki, Sasaki
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: Let $P(x)$ be a given real univariate polynomial and let$?tilde{P}(x)=P(x)+?varDelta(x)$ where $?varDelta(x)$ is the sum oferror terms that is a polynomial with small real unknown but boundedcoefficients. We first consider specifying the ``existence domain''of the values of $?tilde{P}(x)$ or the domain in which the value of$?tilde{P}(x)$ exists for any real number $x$ by the coefficientbounds for $?varDelta(x)$ and then introduce a concept of an``approximate real zero-point'' of $?tilde{P}(x)$. We present apractical method for estimating the existence domain of zero-points of$?tilde{P}(x)$ by applying Smith's celebrated theorem. We nextconsider counting the number of real zero-points of $?tilde{P}(x)$.If all the zero-points are sufficiently far apart from each other thenumber of real zero-points of $?tilde{P}(x)$ is the same as that of$P(x)$ and we derive a condition for which we can assert that $P(x)$and $?tilde{P}(x)$ have the same number of real zero-points. Wecalculate the actual number of real zero-points by Sturm's method which encounters the so-called small leading coefficient problem. Forthis problem we show that under some conditions small leading termscan be discarded. Furthermore we investigate four methods forevaluating the effect of error terms on the elements of the Sturmsequence.
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: Let $P(x)$ be a given real univariate polynomial and let$\tilde{P}(x)=P(x)+\varDelta(x)$, where $\varDelta(x)$ is the sum oferror terms, that is, a polynomial with small real unknown but boundedcoefficients. We first consider specifying the ``existence domain''of the values of $\tilde{P}(x)$, or the domain in which the value of$\tilde{P}(x)$ exists for any real number $x$, by the coefficientbounds for $\varDelta(x)$, and then introduce a concept of an``approximate real zero-point'' of $\tilde{P}(x)$. We present apractical method for estimating the existence domain of zero-points of$\tilde{P}(x)$ by applying Smith's celebrated theorem. We nextconsider counting the number of real zero-points of $\tilde{P}(x)$.If all the zero-points are sufficiently far apart from each other, thenumber of real zero-points of $\tilde{P}(x)$ is the same as that of$P(x)$, and we derive a condition for which we can assert that $P(x)$and $\tilde{P}(x)$ have the same number of real zero-points. Wecalculate the actual number of real zero-points by Sturm's method,which encounters the so-called small leading coefficient problem. Forthis problem, we show that, under some conditions, small leading termscan be discarded. Furthermore, we investigate four methods forevaluating the effect of error terms on the elements of the Sturmsequence.
• 書誌レコードID / 収録物識別子タイプ: NCID
• 書誌レコードID / 収録物識別子: AN00116647
• 書誌情報: 情報処理学会論文誌; 巻 41, 号 4, p. 974-989, 発行日 2000-04-15
• ISSN / 収録物識別子タイプ: ISSN
• ISSN / 収録物識別子: 1882-7764