Numerical Factorization of
Multivariate Complex Polynomials

Andrew J. Sommese, Jan Verschelde, and Charles W. Wampler


One can consider the problem of factoring multivariate complex polynomials as a special case of the decomposition of a pure dimensional solution set of a polynomial system into irreducible components. The importance and nature of this problem however justify a special treatment. We exploit the reduction to the univariate root finding problem as a way to sample the polynomial more efficiently, certify the decomposition with linear traces, and apply interpolation techniques to construct the irreducible factors. With a random combination of differentials we lower multiplicities and reduce to the regular case. Estimates on the location of the zeroes of the derivative of polynomials provide bounds on the required precision. We apply our software to study the singularities of Stewart-Gough platforms.

2000 Mathematics Subject Classification: Primary 13P05, 14A99; Secondary 65H10, 68W30.

keywords: Approximate factorization, divided differences, generic points, homotopy continuation, irreducible decomposition, Newton interpolation, numerical algebraic geometry, monodromy, multiple roots, polynomial, Stewart-Gough platform, symbolic-numeric computation, traces, witness points.

Theoretical Computer Science 315(2-3): 651-669, 2004. Special Issue on Algebraic and Numerical Algorithms edited by I.Z. Emiris, B. Mourrain, and V.Y. Pan.