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The Role of the Fibonacci Sequence in the Isolation of the Real Roots of Polynomial Equations

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Abstract

Isolation of the real roots of polynomials in ℤ[x] is the process of finding real, disjoint intervals each of which contains exactly one real root and every real root is contained in some interval. This process is of interest because, according to Fourier, it constitutes the first step involved in the computation of real roots, the second step being the approximation of these roots to any desired degree of accuracy.

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References

  1. Akritas, A. G. “An Implementation of Vincent’s Theorem.” Numerische Mathematik 36 (1980): pp. 53–62.

    Article  MathSciNet  MATH  Google Scholar 

  2. Akritas, A. G. “The Fastest Exact Algorithms for the Isolation of the Real Roots of a Polynomial Equation. ” Computing 24 (1980): pp. 299–313.

    Article  MathSciNet  MATH  Google Scholar 

  3. Akritas, A. G. “Exact Algorithms for the Implementation of Cauchy’s Rule.” International Journal of Computer Mathematics 9 (1981): pp. 323–333.

    Article  MathSciNet  MATH  Google Scholar 

  4. Akritas, A. G. “Vincent’s Forgotten Theorem, its Extension and Application. ” Inernational Journal of Computer and Mathematics with Applications 7 (1981): pp. 309–317.

    Article  MathSciNet  MATH  Google Scholar 

  5. Akritas, A. G. “Reflections on a Pair of Theorems by Budan and Fourier. ” Mathematics Magazine 55 (1982): pp. 292–298.

    Article  MathSciNet  MATH  Google Scholar 

  6. Akritas, A. G. Elements of Computer Algebra with Applications. J. Wiley Interscience, New York, NY, 1989.

    MATH  Google Scholar 

  7. Akritas, A. G. and Danielopoulos, S. D. “On the Forgotten Theorem of Mr. Vincent. ” Historia Mathematica 5 (1978): pp. 427–435.

    Article  MathSciNet  MATH  Google Scholar 

  8. Chen, Jianhua. “A New Algorithm for the Isolation of Real Roots of Polynomial Equations.” Second International Conference on Computers and Applications, Beijing, P. R. C., June 23–27, 1987, pp. 714–719.

    Google Scholar 

  9. Mahler, K. “An Inequality for the Discriminant of a Polynomial. ” Michigan Mathematical Journal 11 (1964): pp. 257–262.

    Article  MathSciNet  MATH  Google Scholar 

  10. Vincent, A. J. H. “Sur la Résolution des Équations Numériques.” Journal de Mathématiques Pures et Appliquées 1 (1836): pp. 341–372.

    Google Scholar 

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© 1990 Kluwer Academic Publishers

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Akritas, A.G., Bradford, P.G. (1990). The Role of the Fibonacci Sequence in the Isolation of the Real Roots of Polynomial Equations. In: Bergum, G.E., Philippou, A.N., Horadam, A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1910-5_1

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  • DOI: https://doi.org/10.1007/978-94-009-1910-5_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7352-3

  • Online ISBN: 978-94-009-1910-5

  • eBook Packages: Springer Book Archive

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