Computing real zeros of polynomials with parametric coefficients

Authors:
Attilio Colagrossi;Alfonso M. Miola
Affiliations:
Istituto di Analisi dei Sistemi ed Informatica, Roma, Italy;Istituto di Analisi dei Sistemi ed Informatica, Roma, Italy
Venue:
ACM SIGSAM Bulletin
Year:
1983

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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 a real interval Ix for the variable x, the algorithm furnishes a list (eventually empty) of real intervals Iiy for the parameter y, such that there exist i real simple zeros of P(x,y) in the two dimension interval determined by Ix and Iiy.