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CORR
2010
Springer

Improved complexity bounds for real root isolation using Continued Fractions

8 years 12 months ago
Improved complexity bounds for real root isolation using Continued Fractions
We consider the problem of isolating the real roots of a square-free polynomial with integer coefficients using (variants of) the continued fraction algorithm (CF). We introduce a novel way to compute a lower bound on the positive real roots of univariate polynomials. This allows us to derive a worst case bound of OB(d6 + d4 2 + d3 2 ) for isolating the real roots of a polynomial with integer coefficients using the classic variant of CF, where d is the degree of the polynomial and the maximum bitsize of its coefficients. This improves the previous bound by Sharma [30] by a factor of d3 and matches the bound derived by Mehlhorn and Ray [21] for another variant of CF; it also matches the worst case bound of the subdivisionbased solvers. We present a new variant of CF, we call it iCF, that isolates the real roots of a polynomial with integer coefficients in OB(d5 + d4 ), thus improving the current known bound for the problem by a factor of d. If the polynomial has only real roots, then ...
Elias P. Tsigaridas
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2010
Where CORR
Authors Elias P. Tsigaridas
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