2024-10-14T03:23:54Zhttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_oaipmhoai:ipsj.ixsq.nii.ac.jp:002162982022-01-30T23:26:42Z00934:00989:10777:10782
Accelerating the Numerical Computation of Positive Roots of Polynomials Using Suitable Combination of Lower BoundsAccelerating the Numerical Computation of Positive Roots of Polynomials Using Suitable Combination of Lower Boundseng[オリジナル論文] continued fraction method, Vincent's theorem, local-max bound, first-λ boundhttp://id.nii.ac.jp/1001/00216190/Articlehttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_action_common_download&item_id=216298&item_no=1&attribute_id=1&file_no=1Copyright (c) 2022 by the Information Processing Society of JapanNara Women's UniversityKyoto UniversityKyoto UniversityYahoo Japan CorporationUniversity of FukuiOsaka Seikei UniversityMasami, TakataTakuto, AkiyamaSho, ArakiHiroyuki, IshigamiKinji, KimuraYoshimasa, NakamuraThe 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.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.AA11464803情報処理学会論文誌数理モデル化と応用（TOM）15118302022-01-311882-77802022-01-31