A numerical elimination method for polynomial computations

A numerical elimination method is presented in this paper for floating-point computation in polynomial algebra. The method is designed to calculate one or more polynomials in an elimination ideal by a sequence of matrix rank/kernel computation. The method is reliable in numerical computation with verifiable stability and a sensitivity measurement. Computational experiment shows that the method possesses significant advantages over classical resultant computation in numerical stability and in producing eliminant polynomials with lower degrees and fewer extraneous factors. The elimination algorithm combined with an approximate GCD finder appears to be effective in solving polynomial systems for positive dimensional solutions.