Estimation Of Sparse Approximate Greatest Common Divisors Of Several Univariate Polynomials

In this paper,the computation of univariate sparse approximate greatest common divisors(GCDs)is studied.One algorithm in the literature concerning the estimation of sparse approximate GCDs of two input polynomials is extended to the case with multiple input polynomials.Firstly,we discuss the properties of multi-polynomial Sylvester subresultant matrix.And then,we establish a subspace algorithm via the left null space of the multi-polynomial Sylvester subresultant matrix to calculate approximate GCDs.Furthermore,we combine sparse optimization with the subspace algorithm to recover sparse approximate GCDs.Particularly,we present a proof on the uniqueness of the GCDs derived in the subspace algorithm.In numerical experiments,we compare our algorithms with the algorithms in the literature.Numerical experimental results demonstrate the effectiveness and efficiency of our algorithms.