Modified continuous analogue of Newton's method for solving systems of nonlinear equations
Dubna State University, Institute of the system analysis and management; 141980, Dubna, Moscow reg., Universitetskaya str., 19; firstname.lastname@example.org, email@example.com
The construction of effective algorithms for solving systems of two or more nonlinear equations is one of the urgent problems of computational mathematics and its applications.
The paper presents the results of studies of the influence of the iterative parameter in the multidimensional version of the continuous analogue of Newton's method on the area and rate of convergence. An approach is proposed to optimize the convergence process of the continuous analogue of Newton's method (NAMN) for solving systems of nonlinear equations, based on the control of the step size coefficients depending on the behavior of the sign of the coefficients at each iteration and minimizing the residual value from the initial approximation to the root of the equation. Based on this approach, a mechanism for improving the convergence of the continuous analogue of Newton's method for solving systems of nonlinear equations in the case of the Jacobian determinant of the system tends to zero in the vicinity of the exact solution is developed. This mechanism is based on the use of the step change coefficient of the difference scheme as a control parameter. On the basis of the developed mechanism for controlling the convergence process, a modification of the continuous analogue of Newton's method was proposed.