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The article provides general information on nonlinear methods of programming. The algorithm for determining the minimum of various target functions by Newton’s method of the second order is considered. The article presents the main advantages and disadvantages of the method. A circular approximation of the chimney measurement results is performed using Newton's method. The algorithm for solving these tasks was implemented in the Visual Basic for Applications software environment. The comparative analysis was held based on Newton’s method of the second order with the gradient methods for solving engineering and geodetic tasks. The data obtained allow considering the possibility of the further application of Newton’s method in geodesy, especially while solving nonlinear optimization problems. The development of modern technology allows to automate the computing process by writing specific software modules. This makes the process of calculating parameters convenient for the surveyor, as it relieves them from routine calculations.

Application of Newton’s method to solve optimization geodetic tasks