Optimal parametrization in numerical construction of curve

The application of the optimal parametric continuation method to constructing a solution set curve for a system of nonlinear algebraic or transcendental equations depending on a parameter is considered. There are discussed two approaches to solving this problem-the use of iterative methods and reduction to an initial value problem for a system of ordinary differential equations. The algorithm suggested in this paper can also be used for finding an appropriate initial approximation when solving a system of nonlinear algebraic or transcendental equations not depending on a parameter by an iterative method.