Solving Approximate GCD of Multivariate Polynomials By Maple/Matlab/C Combination

The problem of solving approximate GCD of multivariate polynomials has been well studied in the computational literature because of its importance particularly in engineering application[2, 6, 7]. Numbers of algorithms have been proposed to give the approach such as approximate subresultant PRS and modular algorithm using SVD. Here we focus on EZ-GCD[3], another method based on Hensel Lifting. In this computation, QR decomposition of Sylvester Matrix is the key operation. Generally, Computer Algebra Systems such as Maple[9] and Asir/Risa[12] are only applicable in small sized matrix problem. But in multivariate polynomial case, matrix size becomes very large. Obviously it could be more effective if numeric method is adopted. So we must address it in symbolic-numeric combined computation. Moreover, noticing the specificity of Sylvester Matrix data construction[8], more efficient method could be applied if we invoke a C routine acting as Sylvester Matrix QR solver. Hence it is clear that a comprehensive toolkit which can offer faster and more accurate solution on this term is needed. In this paper, Maple, a computer algebra system; Matlab[10], a high-performance numeric library; and C routines, are combined to implement our computation, showing a stable and faster result.