795ddb03-d135-4ba2-a54a-dc47af658c3220210316044459944wseamdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON COMPUTERS1109-275010.37394/23205http://wseas.org/wseas/cms.action?id=40262720202720201910.37394/23205.2020.19http://wseas.org/wseas/cms.action?id=23186Multi-Variant LRP-Polynomials and Homotopy of Polynomial Equations SystemsAleksandrPoliakovPolytechnical Institute, Sevastopol State University, Sevastopol, RUSSIAN FEDERATIONhttps://orcid.org/0000-0002-2940-8945NarinaKolesovaInstitute of Information Technology and Systems and Control Engineering, Sevastopol, RUSSIAN FEDERATIONPavelBugayovMarine Institute, Sevastopol State University, Sevastopol, RUSSIAN FEDERATIONParticular case of nonlinear equations are polynomial equations, solving algorithms of which are justified and investigated in the most detail. However, a general approach to solving such equations and their systems that could be considered universal for solving most practical problems has not yet been developed. This is an incentive to search for new algorithms, adapted, at least, to solve typical applied problems. This paper is devoted to the development the method of Laguerre's type for solving polynomial equations systems with real coefficients. It is shown that this method is close in form to the method of homotopy, which effective, for example, in solving optimization problems of nonconvex functions. Its efficiency and advantages in comparison with the known methods are demonstrated on examples of the study of mathematical models of real objects and processes.41520204152020103110https://www.wseas.org/multimedia/journals/computers/2020/a285103-930.pdf10.37394/23205.2020.19.14http://www.wseas.org/multimedia/journals/computers/2020/a285103-930.pdfS.N. Chow, J. Mallet-Paret, J.A. Yorke,Lecture Notes in Mathematics, in Functional differential equations and approximation of fixed points.Berlin: Springer Verlag, 1979.T.Y. Li, Foundations of Computational Mathematics, in Handbook of Numerical Analysis. Amsterdam:North-Holland, 2003.Y. Li and T. Sauer, Regularity results for solving systems of polynomials by homotopy method, NumericalMathematics, Vol. 50, No. 3, 1987,pp. 283-289.10.1137/0729067T.Y. Li and X. Wang, Nonlinear homotopies for solving deficient polynomial systems with parameters, SIAM Journal on Numerical Analysis, Vol. 29, No. 4, 1992,pp. 1104-1118.10.1137/s0036142903430463A.J. Sommese, J. Verschelde, C.W. Wampler, Homotopies for intersecting solution components of polynomial systems, SIAM Journal on Numerical Analysis, Vol. 42, No. 4, 2004, pp. 1552-1571.C.W. Wampler and A.P. Morgan, Solving the kinematics of general 6R manipulators using polynomial continuation, in Robotics: Applied Mathematics and Computational Aspects, Oxford: Clarendon Press, 1993.C.-H. Parkand H.-T. Shim, What is the homotopy method for a system of nonlinear equations (survey), Journal of Applied Mathematics and Computing, Vol. 17, No. 1-2-3, 2005,pp. 689-700.10.1109/icsmc.2010.5641786O. Poliakov, M. Kolesova, Y. Pashkov, M. Kalinin, V. Kramar, Manipulator synthesis on the given properties of working space. Application of polynomials with linear real parameter, Proc. 2010 IEEE Int Conf on System, Man and Cybernetics, Istanbul, Turkye, 2010, pp. 4325-4332.A.M. Poliakov, Applications of a new numerical method for solving polynomial equations systems to problems of kinematics of hinge mechanisms, New Materialand Technologyin Metallurgyand MechanicalEngineerig, Vol. 1, 2012,pp. 120-126.E. Hansen andM. Patrick, A family of root finding methods, NumericalMathematics, Vol. 27, 1977,pp. 257-269.O.N. Tikhonov, On the fast calculation of largest roots of a polynomial, Notes of Leningrad Institute name after G.V. Plekhanov, Vol. XLVIII, No. 3, 1968, pp. 36-41.A. Polyakov, A numerical solving algorithm for polynomial equation systems, Proc. of the 5th Triennial ETAI Int Conf on Applied Automatic Systems (AAS) 2009, Macedonia, Ohrid, 2009, pp. 109-112.J.M. Ortegaand W.C. Rheinboldt, Iterative solution of nonlinear equation in several variables,N.-Y -London: Academic Press, 1970.10.1145/29380.29862R.P. Kearfott, Some tests of generalized bisection, ACM Transactions on Mathematical Software, Vol. 13, No. 3, 1987,pp. 197-220.