Approximate GCD and its application to ill-conditioned algebraic equations
ISCM '90 Proceedings of the International Symposium on Computation mathematics
The singular value decomposition for polynomial systems
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Approximate polynomial greatest common divisors and nearest singular polynomials
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Optimization strategies for the approximate GCD problem
ISSAC '98 Proceedings of the 1998 international symposium on Symbolic and algebraic computation
The ERES method for computing the approximate GCD of several polynomials
Applied Numerical Mathematics
Approximate polynomial gcd: Small degree and small height perturbations
Journal of Symbolic Computation
Approximate polynomial GCD over integers
Journal of Symbolic Computation
A hybrid approach for normal factorization of polynomials
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
The computation of multiple roots of a polynomial
Journal of Computational and Applied Mathematics
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The computation of the greatest common divisor (GCD) of many polynomials is a nongeneric problem. Techniques defining ''approximate GCD'' solutions have been defined, but the proper definition of the ''approximate'' GCD, and the way we can measure the strength of the approximation has remained open. This paper uses recent results on the representation of the GCD of many polynomials, in terms of factorisation of generalised resultants, to define the notion of ''approximate GCD'' and define the strength of any given approximation by solving an optimisation problem. The newly established framework is used to evaluate the performance of alternative procedures which have been used for defining approximate GCDs.