Browsing by Author "Akritas, A. G."
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Advances on the continued fractions method using better estimations of positive root bounds
Akritas, A. G.; Strzeboński, A. W.; Vigklas, P. S. (2007)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 ... 
Applications of singularvalue decomposition (SVD)
Akritas, A. G.; Malaschonok, G. I. (2004)Let A be an m x n matrix with m greater than or equal to n. Then one form of the singularvalue decomposition of A is A = UT SigmaV, where U and V are orthogonal and Sigma is square diagonal. That is, UUT = Irank(A), VVT ... 
A comparison of various methods for computing bounds for positive roots of polynomials
Akritas, A. G.; Vigklas, P. S. (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 ... 
Computations in modules over commutative domains
Akritas, A. G.; Malaschonok, G. I. (2007)This paper is a review of results on computational methods of linear algebra over commutative domains. Methods for the following problems are examined: solution of systems of linear equations, computation of determinants, ... 
Counting the number of real roots in an interval with Vincent's theorem
Akritas, A. G.; Vigklas, P. S. (2010)It is well known that, in 1829, the French mathematician Jacques Charles Francois Sturm (18031855) solved the problem of finding the number of real roots of a polynomial equation f(x) = 0, with rational coefficients and ... 
Foreword to the special issue on applications of computer algebra
Kotsireas, I. S.; Akritas, A. G.; Steinberg, S. L.; Wester, M. J. (2005) 
Improving the Performance of the Continued Fractions Method Using New Bounds of Positive Roots
Akritas, A. G.; Strzebonski, A. W.; Vigklas, P. S. (2008)In this paper we compare four implementations of the VincentAkritasStrzebonski Continued Fractions (VASCF) real root isolation method using four different (two linear and two quadratic complexity) bounds on the values ... 
Linear and Quadratic Complexity Bounds on the Values of the Positive Roots of Polynomials
Akritas, A. G. (2009)In this paper we review the existing linear and quadratic complexity (upper) bounds on the values of the positive roots of polynomials and their impact on the performance of the VincentAkritasStrzebonski (VAS) continued ... 
Vincent's theorem of 1836: Overview and future research
Akritas, A. G. (2010)In this paper, we present two different versions of Vincent's theorem of 1836 and discuss various real root isolation methods derived from them: one using continued fractions and two using bisections, the former being the ...