scholarly journals Univariate Polynomial Real Root Isolation: Continued Fractions Revisited

2006 ◽  
pp. 817-828 ◽  
Author(s):  
Elias P. Tsigaridas ◽  
Ioannis Z. Emiris
Keyword(s):  
Continued Fractions ◽  
Real Root ◽  
Root Isolation ◽  
Univariate Polynomial ◽  
Polynomial Real Root Isolation ◽  
Real Root Isolation

scholarly journals On the complexity of real root isolation using continued fractions

2008 ◽  
Vol 392 (1-3) ◽  
pp. 158-173 ◽  
Author(s):  
Elias P. Tsigaridas ◽  
Ioannis Z. Emiris
Keyword(s):  
Continued Fractions ◽  
Real Root ◽  
Root Isolation ◽  
Real Root Isolation

scholarly journals Improving the Performance of the Continued Fractions Method Using New Bounds of Positive Roots

2008 ◽  
Vol 13 (3) ◽  
pp. 265-279 ◽  
Author(s):  
A. G. Akritas ◽  
A. W. Strzebonski ◽  
P. S. Vigklas
Keyword(s):  
Continued Fractions ◽  
Real Root ◽  
Isolation Method ◽  
Complexity Bounds ◽  
Positive Roots ◽  
Speed Up ◽  
Root Isolation ◽  
Roots Of Polynomials ◽  
Real Root Isolation

In this paper we compare four implementations of the Vincent-AkritasStrzebo´nski Continued Fractions (VAS-CF) real root isolation method using four different (two linear and two quadratic complexity) bounds on the values of the positive roots of polynomials. The quadratic complexity bounds were included to see if the quality of their estimates compensates for their quadratic complexity. Indeed, experimentation on various classes of special and random polynomials revealed that the VAS-CF implementation using LMQ, the Quadratic complexity variant of our Local Max bound, achieved an overall average speed-up of 40 % over the original implementation using Cauchy’s linear bound.

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