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IASI Research Report n. 26 (Previous Next) Colagrossi A.,

Miola A.A generalization of Sturm's method for computing real zeros of polynomials with parametric coefficients.ABSTRACT The problem of localizing real zeros of polynomials with parametric coefficients is considered.
An informative solution to this problem is proposed and an algorithm based on a generalization of Sturm's method for univariate polynomials over the reals is presented. Thus, given a polynomial P(x,y), where x is the variable and y a parameter, and an open real interval I_x for the variable x, the algorithm furnishes a list (eventually empty) of real intervals I_{iy} for the parameter y, such that there exist i real simple zeros of P(x,y) in the two dimension interval determined by I_x and I_{iy}.