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Accelerating the Numerical Computation of Positive Roots of Polynomials Using Suitable Combination of Lower Bounds
en
[オリジナル論文] continued fraction method, Vincent's theorem, local-max bound, first-λ bound
Nara Women's University
Kyoto University
Kyoto University
Yahoo Japan Corporation
University of Fukui
Osaka Seikei University
Masami Takata
Takuto Akiyama
Sho Araki
Hiroyuki Ishigami
Kinji Kimura
Yoshimasa Nakamura
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.
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）
15
1
18-30
2022-01-31
1882-7780