Bounds for real roots and applications to orthogonal polynomials

Authors:
Doru Ştefănescu
Affiliations:
University of Bucharest, Romania
Venue:
CASC'07 Proceedings of the 10th international conference on Computer Algebra in Scientific Computing
Year:
2007

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Abstract

We obtain new inequalities on the real roots of a univariate polynomial with real coefficients. Then we derive estimates for the largest positive root, which is a key step for real root isolation. We discuss the case of classic orthogonal polynomials. We also compute upper bounds for the roots of orthogonal polynomials using new inequalities derived from the differential equations satisfied by these polynomials. Our results are compared with those obtained by other methods.