A Subspace Algorithm For Computing One Kind Of Greatest Common Divisors Of Multivariate Polynomials

The calculation of greatest common divisor of polynomials is a fundamental problem in the field of computational mathematics.In practical applications,many problems in-volve the calculation of greatest common divisor of polynomials.Therefore,it is of great significance to establish an effective algorithm for solving this problem.This paper con-cerns the calculation of approximate greatest common divisor of two multivariate polyno-mials with noisy coefficients,and a subspace algorithm for computing greatest common divisor of univariate polynomials in the literature is extended to multivariate polynomials,and a subspace algorithm for computing greatest common divisor of one special kind of multivariate polynomials is established.The algorithm is established based on the similar-ity between greatest common divisor of this special kind of multivariate polynomials and that of univariate polynomials.In the numerical experiments,we compare the proposed algorithm in the paper with existing algorithms in the literature.Numerical experimental results show that the algorithm in this paper is effective and is more stable in some sense.