Allgower, Eugene L.; Georg, Kurt; Miranda, Rick The method of resultants for computing real solutions of polynomial systems. (English) Zbl 0756.65077 SIAM J. Numer. Anal. 29, No. 3, 831-844 (1992). The problem of finding the real zeros in a prescribed \(n\)-dimensional rectangle for polynomial systems having real coefficients is considered. A new method based on the theory of multiresultants is proposed. The inherently unstable calculation of the determinant is replaced by a stable minimization procedure, which is able to take advantage of the sparseness of the resultant matrix. Two numerical examples illustrate the method. Reviewer: V.A.Kostova (Russe) Cited in 10 Documents MSC: 65H10 Numerical computation of solutions to systems of equations 65H20 Global methods, including homotopy approaches to the numerical solution of nonlinear equations 26C10 Real polynomials: location of zeros 12Y05 Computational aspects of field theory and polynomials (MSC2010) Keywords:conjugate gradient method; Lanczos method; real zeros; polynomial systems; multiresultants; resultant matrix; numerical examples PDFBibTeX XMLCite \textit{E. L. Allgower} et al., SIAM J. Numer. Anal. 29, No. 3, 831--844 (1992; Zbl 0756.65077) Full Text: DOI Link