New Laguerre-s Type Method for Solving of a Polynomial Equations Systems
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New Laguerre-s Type Method for Solving of a Polynomial Equations Systems

Authors: Oleksandr Poliakov, Yevgen Pashkov, Marina Kolesova, Olena Chepenyuk, Mykhaylo Kalinin, Vadym Kramar

Abstract:

In this paper we present a substantiation of a new Laguerre-s type iterative method for solving of a nonlinear polynomial equations systems with real coefficients. The problems of its implementation, including relating to the structural choice of initial approximations, were considered. Test examples demonstrate the effectiveness of the method at the solving of many practical problems solving.

Keywords: Iterative method, Laguerre's method, Newton's method, polynomial equation, system of equations

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1085022

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[1] G.N. Vanderplaats, Numerical Optimization Techniques for Engineering Design: With Applications, New York: McGraw Hill, 1984.
[2] R.T. Haftka, and Z. Gurdal, Elements of Structural Optimization, Dordrecht: Kluwer Academic Publishers, 1992.
[3] R. Aviles, G. Ajuria, V. Gomez-Garay, and S. Navalpotro, "Comparison Among Nonlinear Optimization Methods for the Static Equilibrium Analysis of Multibody Systems With Rigid And Elastic Elements," Mechanism and Machine Theory, vol. 35, no. 8, pp. 1151-1168, August 2000.
[4] Y. Luo, X. Fan, D. Li, and X. Wu, "Hyper-Chaotic Mapping Newton Iterative Method to Mechanism Synthesis," Journal of Mechanical Engineering, vol. 54, no. 5, pp. 372-378, 2008.
[5] A. Hernandez, , and V. Petuya, "Position Analysis of Planar Mechanisms With R-Pairs Using a Geometrical-Iterative Method," Mechanism and Machine Theory, vol. 39, no. 2, pp. 133-152, February 2004,
[6] U.S. Chavan, and S.V. Joshi, "Synthesis And Analysis of Coupler Curves With Combined Planar Cam Follower Mechanisms," International Journal of Engineering, Science and Technology, vol. 2, no. 6, pp. 231-243, 2010.
[7] A.E. Albanesi, V.D. Fachinotti, and M.A. Pucheta, "Review on Design Methods for Compliant Mechanisms," Mecanica Computacional, vol. XXIX, pp. 59-72, November 2010.
[8] A. Polyakov, and M. Polyakova, "Recurrent Formula for Finding of a Real Roots of a Nonlinear Algebraic Equations In Application to the Problems of a Mechanisms Mechanics," New materials and technologies in metallurgy and mechanical engineering, no. 2, pp. 93- 96, 2002.
[9] J.M. Ortega, and W.C. Rheinboldt, Iterative Solution of nonlinear equation in several variables. New York - London: Academic Press, 1970.
[10] E. Hansen, and M. Patric, "A Family of Root Finding Methods," Numerical Mathematics, vol. 27, no. 3, pp. 257-269, 1976/1977.
[11] O. Tikhonov, "On the Rapid Computation of the Largest Zeros of a Polynomial," Notes of the Leningrad Mining Institute, vol. 48, no. 3, pp.98-103, 1968.
[12] A. Polyakov, M. Kolesova, M. Kalinin, and P. Shtanko, "Algorithm of Numerical Solving of the Nonlinear Algebraic Equations in the Conditions of Absence of the Information-s About Neighbourhoods of Roots," in Proc. volume from the 6-th IFAC workshop DECOM-TT 2009, Scopje, 2009, pp. 301-306.
[13] A. Polyakov, "A Numerical Solving Algorithm for Polynomial Equation Systems," in Proc. of Selected AAS 2009 Conf. Papers, Scopje-Istanbul, 2009, pp. 109-112.
[14] A. Polyakov, M. Kolesova, M. Kalinin, and V. Kramar, "Manipulator Synthesis on the Given Properties of Working Space. Application of Polynomials with Linear Real Parameter," in Proc. of 2010 IEEE International Conference on Systems Man and Cybernetics (SMC), Istanbul, 2010, pp. 4325-4332.
[15] R.P. Kearfott, "Some Tests of Generalized Bisection," ACM Transactions on Mathematical Software, vol. 13, no. 3, pp.197-220, September 1987.