Numerical and Symbolical Methods for the GCD of Several Polynomials

Christou, D., Karcanias, N., Mitrouli, M. & Triantafyllou, D. (2011). Numerical and Symbolical Methods for the GCD of Several Polynomials. Lecture Notes in Electrical Engineering, 80, pp. 123-144. doi: 10.1007/978-94-007-0602-6

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The computation of the Greatest Common Divisor (GCD) of a set of polynomials is an important issue in computational mathematics and it is linked to Control Theory very strong. In this paper we present different matrix-based methods, which are developed for the efficient computation of the GCD of several polynomials. Some of these methods are naturally developed for dealing with numerical inaccuracies in the input data and produce meaningful approximate results. Therefore, we describe and compare numerically and symbolically methods such as the ERES, the Matrix Pencil and other resultant type methods, with respect to their complexity and effectiveness. The combination of numerical and symbolic operations suggests a new approach in software mathematical computations denoted as hybrid computations. This combination offers great advantages, especially when we are interested in finding approximate solutions. Finally the notion of approximate GCD is discussed and a useful criterion estimating the strength of a given approximate GCD is also developed.

Item Type: Article
Additional Information: The final publication is available at Springer via
Uncontrolled Keywords: Greatest Common Divisor, Gaussian elimination, Resultant, MatrixPencil, Singular Value Decomposition, symbolic-numeric computations
Subjects: T Technology > TK Electrical engineering. Electronics Nuclear engineering
Divisions: School of Engineering & Mathematical Sciences > Engineering

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