Accelerating the Numerical Computation of Positive Roots of Polynomials using Improved Bounds

• Item type: SIG Technical Reports(1)
• 公開日: 2014-07-14
• タイトル: Accelerating the Numerical Computation of Positive Roots of Polynomials using Improved Bounds
• タイトル / 言語: en
• タイトル: Accelerating the Numerical Computation of Positive Roots of Polynomials using Improved Bounds
• 言語: eng
• 資源タイプ / 資源タイプ識別子: http://purl.org/coar/resource_type/c_18gh
• 資源タイプ: technical report
• 著者所属: Graduate School of Informatics, Kyoto University
• 著者所属: Graduate School of Informatics, Kyoto University
• 著者所属: Graduate School of Informatics, Kyoto University
• 著者所属: Academic Group of Information and Computer Sciences, Nara Women's University
• 著者所属: Graduate School of Informatics, Kyoto University
• 著者所属(英): en
• 著者所属(英): Graduate School of Informatics, Kyoto University
• 著者所属(英): en
• 著者所属(英): Graduate School of Informatics, Kyoto University
• 著者所属(英): en
• 著者所属(英): Graduate School of Informatics, Kyoto University
• 著者所属(英): en
• 著者所属(英): Academic Group of Information and Computer Sciences, Nara Women's University
• 著者所属(英): en
• 著者所属(英): Graduate School of Informatics, Kyoto University
• 著者名: Kinji, Kimura; Takuto, Akiyama; Hiroyuki, Ishigami; Masami, Takata; Yoshimasa, Nakamura
• 著者名(英): Kinji, Kimura; Takuto, Akiyama; Hiroyuki, Ishigami; Masami, Takata; Yoshimasa, Nakamura
• 論文抄録 / 内容記述タイプ: Other
• 論文抄録 / 内容記述: The continued fraction method for isolating the positive roots of a univariate polynomial equation is based on Vincent's theorem, which computes all of the real roots of polynomial equations. In this paper, we propose two new lower bounds which accelerate the fraction method. The two proposed bounds are derived from a theorem stated by Akritas et al., and use different pairing strategies for the coefficients of the target polynomial equations from the bounds proposed by Akritas et al. Numerical experiments show that the proposed lower bounds are more effective than existing bounds for some special polynomial equations and random polynomial equations, and are competitive with them for other special polynomial equations.
• 論文抄録(英) / 内容記述タイプ: Other
• 論文抄録(英) / 内容記述: The continued fraction method for isolating the positive roots of a univariate polynomial equation is based on Vincent's theorem, which computes all of the real roots of polynomial equations. In this paper, we propose two new lower bounds which accelerate the fraction method. The two proposed bounds are derived from a theorem stated by Akritas et al., and use different pairing strategies for the coefficients of the target polynomial equations from the bounds proposed by Akritas et al. Numerical experiments show that the proposed lower bounds are more effective than existing bounds for some special polynomial equations and random polynomial equations, and are competitive with them for other special polynomial equations.
• 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: AN10505667
• 書誌情報: 研究報告数理モデル化と問題解決（MPS）; 巻 2014-MPS-99, 号 6, p. 1-4, 発行日 2014-07-14
• Notice: SIG Technical Reports are nonrefereed and hence may later appear in any journals, conferences, symposia, etc.
• 出版者 / 言語: ja
• 出版者: 情報処理学会