Integer Arithmetic Algorithms for Polynomial Real Zero Determination
Journal of the ACM (JACM)
Polynomial real root isolation by differentiation
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
Polynomial real root isolation using Descarte's rule of signs
SYMSAC '76 Proceedings of the third ACM symposium on Symbolic and algebraic computation
A short note on a new method for polynomial real root isolation
ACM SIGSAM Bulletin
Complete numerical isolation of real zeros in zero-dimensional triangular systems
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
On the computing time of the continued fractions method
Journal of Symbolic Computation
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A new method is presented for the isolation of the real roots of a given integral, univariate, square-free polynomial P. This method is based on Vincent's theorem and only uses: (i) Descartes' rule of signs, and (ii) transformations of the form x = a1 + 1/x′, x′ = a2 + 1/x″, x″ = a3 + 1/x‴, ..., for positive, integral ai's. The key element in this procedure is the calculation of the quantities a1, a2, a3,... . We compute them as "positive lower root bounds" of polynomials and the resulting algorithm has the best theoretical computing time achieved thus far. Empirical results also verify the superiority of our method over all others existing.