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Bounds for Real Roots and Applications to Orthogonal Polynomials

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Book cover Computer Algebra in Scientific Computing (CASC 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4770))

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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.

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Authors and Affiliations

  1. University of Bucharest, Romania

    Doru Ştefănescu

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  1. Doru Ştefănescu
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Victor G. Ganzha Ernst W. Mayr Evgenii V. Vorozhtsov

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Ştefănescu, D. (2007). Bounds for Real Roots and Applications to Orthogonal Polynomials. In: Ganzha, V.G., Mayr, E.W., Vorozhtsov, E.V. (eds) Computer Algebra in Scientific Computing. CASC 2007. Lecture Notes in Computer Science, vol 4770. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75187-8_30

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  • DOI: https://doi.org/10.1007/978-3-540-75187-8_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-75186-1

  • Online ISBN: 978-3-540-75187-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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