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Localization of Roots of a Polynomial not Represented in Canonical Form

In: Computer Algebra in Scientific Computing CASC’99

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  • Alexei Yu Uteshev

    (St. Petersburg State University, Faculty of Applied Mathematics)

Abstract

The root isolation problem for the polynomial equation not represented in the canonical form can sometimes be solved without evaluation of the coefficients of powers of the variable. We investigate the approach based on representing first the equation in the equivalent determinantal (Hankel or block Hankel) form, and employing then Hermite’s root separation method. We illustrate this for the problems of eigenvalues localization, estimation of sensitivity of the roots of the parameter dependent polynomial and nonlinear optimization.

Suggested Citation

  • Alexei Yu Uteshev, 1999. "Localization of Roots of a Polynomial not Represented in Canonical Form," Springer Books, in: Victor G. Ganzha & Ernst W. Mayr & Evgenii V. Vorozhtsov (ed.), Computer Algebra in Scientific Computing CASC’99, pages 431-440, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-60218-4_33
    DOI: 10.1007/978-3-642-60218-4_33
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