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Finding roots of nonlinear equations using the method of concave support functions

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Abstract

A method for finding roots of nonlinear equations on a closed interval generalizing Newton’s method is proposed. The class of functions for which the proposed method is convergent, is determined. The rate of convergence is estimated and results of a numerical simulation are given.

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References

  1. O. V. Khamisov, “Finding the real roots of a polynomial on a closed interval using the method of concave support functions,” in Optimization, Control, Intellect (IDSTU, Irkutsk, 1999), Vol. 3, pp. 167–177 [in Russian].

    Google Scholar 

  2. N. N. Kalitkin, Numerical Methods (Nauka, Moscow, 1978) [in Russian].

    Google Scholar 

  3. G. P. Kutishchev, Solution of Algebraic Equations of Arbitrary Degree (Izd. LKI, Moscow, 2010) [in Russian].

    Google Scholar 

  4. A. V. Khlyamkov, “A remark on the convergence of the parabola method,” Mat. Zametki 63 (2), 309 (1998) [Math. Notes 63 (1–2), 271–272 (1998)].

    Article  MathSciNet  Google Scholar 

  5. Ya. D. Sergeev and D. E. Kvasov, Diagonal Methods of Global Optimization (Fizmatlit, Moscow, 2008) [in Russian].

    Google Scholar 

  6. A. Molinaro and Y. D. Sergeev, “Finding the minimal root of an equation with the multiextremal and nondifferentiable left-hand side,” Numer. Algorithms 28 (1-4), 255–272 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  7. O. V. Khamisov, “Global optimization of functions with concave support minorant,” Comput. Math. Math. Phys. 44, No. 9, 1473–1483 (2004). Zh. Vychisl. Mat. Mat. Fiz. 44 (9), 1552–1563 (2004) [Comput. Math. Math. Phys. 44 (9), 1473–1483 (2004)].

    MathSciNet  Google Scholar 

  8. V. G. Karmanov, Mathematical Programming (Fizmatlit, Moscow, 2000) [in Russian].

    MATH  Google Scholar 

  9. R. Horst and H. Tuy, Global Optimization: Deterministic Approaches (Springer-Verlag, Berlin, 1996).

    Book  MATH  Google Scholar 

  10. J. E. Dennis, jr., and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice-Hall, Englewood Cliffs, NJ, 1983; Mir, Moscow, 1988).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Melent’ev Institute of Power Systems, Siberian Branch, Russian Academy of Sciences, Irkutsk, Russia

    O. V. Khamisov

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  1. O. V. Khamisov
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Correspondence to O. V. Khamisov.

Additional information

Original Russian Text © O. V. Khamisov, 2015, published in Matematicheskie Zametki, 2015, Vol. 98, No. 3, pp. 427–435.

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Khamisov, O.V. Finding roots of nonlinear equations using the method of concave support functions. Math Notes 98, 484–491 (2015). https://doi.org/10.1134/S000143461509014X

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  • DOI: https://doi.org/10.1134/S000143461509014X

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