Generalized companion matrix for approximate GCD

Details Generalized companion matrix for approximate GCD Generalized companion matrix for approximate GCD

2011-02-09

arxiv.org/abs/1102.1809v1

Computer Science

Symbolic Computation

Submitted to MEGA 2011

Scientific paper

We study a variant of the univariate approximate GCD problem, where the coe?- cients of one polynomial f(x)are known exactly, whereas the coe?cients of the second polynomial g(x)may be perturbed. Our approach relies on the properties of the matrix which describes the operator of multiplication by gin the quotient ring C[x]=(f). In particular, the structure of the null space of the multiplication matrix contains all the essential information about GCD(f; g). Moreover, the multiplication matrix exhibits a displacement structure that allows us to design a fast algorithm for approximate GCD computation with quadratic complexity w.r.t. polynomial degrees.

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