Matrix representation of the shifting operation and numerical properties of the ERES method for computing the greatest common divisor of sets of many polynomials

Christou, D., Karcanias, N. & Mitrouli, M. (2014). Matrix representation of the shifting operation and numerical properties of the ERES method for computing the greatest common divisor of sets of many polynomials. Journal of Computational and Applied Mathematics, 260, pp. 54-67. doi: 10.1016/j.cam.2013.09.021

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Abstract

The Extended-Row-Equivalence and Shifting (ERES) method is a matrix-based method developed for the computation of the greatest common divisor (GCD) of sets of many polynomials. In this paper we present the formulation of the shifting operation as a matrix product which allows us to study the fundamental theoretical and numerical properties of the ERES method by introducing its complete algebraic representation. Then, we analyse in depth its overall numerical stability in finite precision arithmetic. Numerical examples and comparison with other methods are also presented.

Item Type: Article
Additional Information: Preprint version.
Uncontrolled Keywords: Univariate real polynomials, greatest common divisor, shifting operation, numerical stability
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: School of Engineering & Mathematical Sciences > Engineering
URI: http://openaccess.city.ac.uk/id/eprint/2944

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