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The method of resultants for computing real solutions of polynomial systems. (English) Zbl 0756.65077

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.

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)
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