Multi-Variant LRP-Polynomials and Homotopy of Polynomial Equations Systems

Particular 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.