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Computing approximate GCD of univariate polynomials by structured total least norm

By Lihong Zhi and Zhengfeng Yang


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

Year: 2004
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