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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)

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 3 , or any of its… (More)

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. S ¸tef˘ anescu's recently published theorem offers an alternative, but unfortunately is of limited applicability as it… (More)

- Panagiotis S. Vigklas, Panagiotis Sakkalis
- 2011

To my parents ii ACKNOWLEDGEMENTS Heartfelt thanks go to my scientific adviser, Prof. Alkiviadis Akritas for making me familiar with computer algebra systems and root isolation methods, for his patient support and his indefatigable interest in my thesis and for his friendship. I am deeply indebted to Adam Strzebo´nski and Prof. Doru S ¸tef˘ anescu for their… (More)

In this talk we first mention some key facts of Obreschkoff's life and work and then delve into the influence of Obreschkoff's book Verteilung und Berechnung der Nullstellen reeller Polynome, VEB Deutscher Verlag der Wissenschaften, Berlin, 1963, on the real root isolation problem. Obreschkoff is one of only two authors in the literature (Uspensky being the… (More)

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