Accelerating the Numerical Computation of Positive Roots of Polynomials Using Suitable Combination of Lower Bounds

• Item type: Trans(1)
• 公開日: 2022-01-31
• タイトル: Accelerating the Numerical Computation of Positive Roots of Polynomials Using Suitable Combination of Lower Bounds
• タイトル / 言語: en
• タイトル: Accelerating the Numerical Computation of Positive Roots of Polynomials Using Suitable Combination of Lower Bounds
• 言語: eng
• キーワード / 主題Scheme: Other
• キーワード / 主題: [オリジナル論文] continued fraction method, Vincent's theorem, local-max bound, first-λ bound
• 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
• 著者所属: Nara Women's University
• 著者所属: Kyoto University
• 著者所属: Kyoto University
• 著者所属: Yahoo Japan Corporation
• 著者所属: University of Fukui
• 著者所属: Osaka Seikei University
• 著者所属(英): en
• 著者所属(英): Nara Women's University
• 著者所属(英): en
• 著者所属(英): Kyoto University
• 著者所属(英): en
• 著者所属(英): Kyoto University
• 著者所属(英): en
• 著者所属(英): Yahoo Japan Corporation
• 著者所属(英): en
• 著者所属(英): University of Fukui
• 著者所属(英): en
• 著者所属(英): Osaka Seikei University
• 著者名: Masami, Takata; Takuto, Akiyama; Sho, Araki; Hiroyuki, Ishigami; Kinji, Kimura; Yoshimasa, Nakamura
• 著者名(英): Masami, Takata; Takuto, Akiyama; Sho, Araki; Hiroyuki, Ishigami; Kinji, Kimura; 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 suitable combination of 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. Moreover, we compute another bound. First, we compute a candidate for the lower bound generated by Newton's method. Second, by using Laguerre's theorem, we check whether the candidate for the lower bound is appropriate. Numerical experiments show that the three 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. Additionally, we determine a suitable combination of those lower bounds.
• 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 suitable combination of 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. Moreover, we compute another bound. First, we compute a candidate for the lower bound generated by Newton's method. Second, by using Laguerre's theorem, we check whether the candidate for the lower bound is appropriate. Numerical experiments show that the three 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. Additionally, we determine a suitable combination of those lower bounds.
• 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: AA11464803
• 書誌情報: 情報処理学会論文誌数理モデル化と応用（TOM）; 巻 15, 号 1, p. 18-30, 発行日 2022-01-31
• ISSN / 収録物識別子タイプ: ISSN
• ISSN / 収録物識別子: 1882-7780
• 出版者 / 言語: ja
• 出版者: 情報処理学会