2023-09-25T15:00:49Zhttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_oaipmhoai:ipsj.ixsq.nii.ac.jp:001021662023-04-27T10:00:04Z01164:02735:07461:07623
Accelerating the Numerical Computation of Positive Roots of Polynomials using Improved BoundsAccelerating the Numerical Computation of Positive Roots of Polynomials using Improved Boundsenghttp://id.nii.ac.jp/1001/00102143/Technical Reporthttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_action_common_download&item_id=102166&item_no=1&attribute_id=1&file_no=1Copyright (c) 2014 by the Information Processing Society of JapanGraduate School of Informatics, Kyoto UniversityGraduate School of Informatics, Kyoto UniversityGraduate School of Informatics, Kyoto UniversityAcademic Group of Information and Computer Sciences, Nara Women's UniversityGraduate School of Informatics, Kyoto UniversityKinji, KimuraTakuto, AkiyamaHiroyuki, IshigamiMasami, TakataYoshimasa, 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 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.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.AN10505667研究報告数理モデル化と問題解決（MPS）2014-MPS-996142014-07-142014-07-04