The resultants method for approximating real fixed points of polynomials

We present a new method for computing the real fixed points of polynomials using the resultants method. It is based on the theory of multi-resultants. The unstable calculation of the determinant of the large sparse matrix is replaced by a stable minimization problem using the Lanczos method. This technique will be able to take advantage of the sparseness of the resultant matrix. Algorithms and numerical results are presented.