Computing Approximate GCD of Univariate Polynomials by Structure Total Least Norm
نویسندگان
چکیده
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 2-GCD for a given tolerance 2. 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.
منابع مشابه
Structured Low Rank Approximation of a Sylvester Matrix
The task of determining the approximate greatest common divisor (GCD) of univariate polynomials with inexact coefficients can be formulated as computing for a given Sylvester matrix a new Sylvester matrix of lower rank whose entries are near the corresponding entries of that input matrix. We solve the approximate GCD problem by a new method based on structured total least norm (STLN) algorithms...
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