Variable projection methods for approximate (greatest) common divisor computations. Vrije Universiteit Brussel
We consider the problem of finding for a given N-tuple of polynomials (real or complex) the closest N-tuple that has a common divisor of degree at least d. Extended weighted Euclidean seminorm of the coefficients is used as a measure of closeness. Two equivalent representations of the problem are considered: (i) direct parameterization over the common divisors and quotients (image representation), and (ii) Sylvester low-rank approximation ...