Numerical and symbolical comparison of resultant type, ERES and MP methods computing the Greatest Common Divisor of several polynomials

In this paper we compare different matrix-based numerical methods computing the Greatest Common Divisor (GCD) of several polynomials. More particularly we compare numerically and symbolically resultant type, ERES and MP methods in respect of their complexity and effectiveness. The combination of numerical and symbolic operations suggests a new approach in software mathematical computations denoted as hybrid computations. For some of the above methods their hybrid nature is presented. Finally the notion of approximate GCD is described and a useful criterion estimating the strength of approximation of a computed GCD is also developed.