UDC 519.615
METHOD FOR LOCALIZATION OF ZEROS OF ANALYTIC FUNCTIONS
BASED ON KRAWCZYK OPERATOR
Abstract. Localization of zeros of analytic functions is considered. For this purpose, Krawczyk operator is used. The formulas for calculation of Krawczyk operator are derived. As a result, algorithm for localization of zeros is proposed. Application of the method is shown by numerical examples including search of zeros for Riemann zeta function.
Keywords: nonlinear equation, analytic function, root localization, Krawczyk operator, Taylor’s expansion.
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REFERENCES
- Moore R.E. A test for existence of solutions to nonlinear systems. SIAM J. Numer. Anal. 1977. Vol. 14. P. 611–615.
- Semenov V.Yu. The method of finding all the roots of a system of nonlinear algebraic equations, based on the Kravchik operator. Kibernetika i sistemnyj analiz. 2015. Vol. 51, No. 5. C. 169–175.
- Neumaier A., Zuhe S. The Krawczyk operator and Kantorovich theorem. J. Math. Anal. Applications. 1990. Vol. 149, N 2. P. 437–443.
- Semenov V. Method for the calculation of all zeros of an analytic function based on the Kantorovich theorem. Comput. Methods Appl. Math. 2014. N 3. P. 385–392.
- Kearfott R.B. Rigorous global search: Continuous problems. Dordrecht: Kluwer Academic Publishers, 1996. 264 р.
- Semenov V. Method for the calculation of all non-multiple zeros of an analytic function. Comput. Methods Appl. Math. 2011. N 1. P. 67–74.
