Abstract. The problem of approximating the greatest common divisor(GCD) for polynomials with inexact coefficients can be formulated as a low rank approximation problem with Sylvester matrix. This paper presents a method based on Structured Total Least Norm(STLN) for constructing the nearest Sylvester matrix of given lower rank. We present algorithms for computing the nearest GCD and a certified ɛ-GCD for a given tolerance ɛ. The running time of our algorithm is polynomial in the degrees of polynomials. We also show the performance of the algorithms on a set of univariate polynomials
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