One way to control the convergence process of Newton's iterative method

The short review of the iterative numerical schemes based on Newton's method is provided in work. Comparison of various numerical methods of the Newtonian type is carried out. Influence of iterative parameter in a continuous analog of a method of Newton on area and speed of convergence is investigated. Approach to optimization of process of convergence of the continuous analog of a method of Newton (CAMN) is offered. On the basis of this approach the mechanism of speed control of convergence of a continuous analog of a method of Newton with use as the operating parameter of coefficient of change of a step of the differential scheme for the numerical solution of the differential equation of NAMN is developed. On the basis of the data obtained during the research modification for a continuous analog of a method of Newton has been offered.