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- Alkiviadis G. Akritas, Adam W. Strzebonski, Panagiotis S. Vigklas
- Computing
- 2006

Finding an upper bound for the positive roots of univariate polynomials is an important step of the continued fractions real root isolation algorithm. The revived interest in this algorithm has highlighted the need for better estimations of upper bounds of positive roots. In this paper we present a new theorem, based on a generalization of a theorem by D.… (More)

Abstract. In this paper we compare four implementations of the Vincent-AkritasStrzeboński 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… (More)

Given an m×n matrix A, with m ≥ n, the four subspaces associated with it are shown in Fig. 1 (see [1]). Fig. 1. The row spaces and the nullspaces of A and A T ; a 1 through a n and h 1 through h m are abbreviations of the alignerframe and hangerframe vectors respectively (see [2]). The Fundamental Theorem of Linear Algebra tells us that N (A) is the… (More)

- Alkiviadis G. Akritas, Panagiotis S. Vigklas
- J. UCS
- 2007

The recent interest in isolating real roots of polynomials has revived interest in computing sharp upper bounds on the values of the positive roots of polynomials. Until now Cauchy’s method was the only one widely used in this process. Ştefănescu’s recently published theorem offers an alternative, but unfortunately is of limited applicability as it works… (More)

We present an implementation of the Continued Fractions (CF) real root isolation method using a recently developed upper bound on the positive values of the roots of polynomials. Empirical results presented in this paper verify that this implementation makes the CF method always faster than the Vincent-Collins-Akritas bisection method, or any of its… (More)

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