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

摘要

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.