Abstract
The article considers the theoretical component of Newton’s second-order method, its main advantages and disadvantages when used in geodesy. The algorithm for determining the minimum of target functions by the Newton method of the second order was studied and analyzed in detail. Parameters of connection between flat rectangular coordinate systems are calculated. The task of determining the transition keys is relevant for geodesy. Comparative analysis of Newton’s method with the method of conjugated gradients was carried out. The algorithm for solving this problem was implemented in the Visual Basic for Applications software environment. The obtained data allow us to conclude that the Newton method can be used more widely in geodesy, especially in solving nonlinear optimization problems. However, the successful implementation of the method in geodetic production is possible only if the computational process is automated, by writing software modules in various programming languages to solve a specific problem.
Highlights
In solving some marketing and geodetic problems, the speed of obtaining the determined parameters, as well as automation of the computing process, plays a special role
The development of geodetic instruments has put the solution of many geodetic problems at a new technological level
As is known from the theory of mathematical processing of geodetic measurements, nonlinear problems for which it is necessary to create nonlinear target functions with redundant measurements need to optimize the process of calculating the determined parameters
Summary
In solving some marketing and geodetic problems (scanning moving objects, calculating transition keys, calculating deformations of various structures), the speed of obtaining the determined parameters, as well as automation of the computing process, plays a special role. The development of geodetic instruments has put the solution of many geodetic problems at a new technological level. In his works A.A. Kuzin and others [1], as well as Tsvetkov V. As is known from the theory of mathematical processing of geodetic measurements, nonlinear problems for which it is necessary to create nonlinear target functions with redundant measurements need to optimize the process of calculating the determined parameters. Influence of computer technologies on geodetic production is noted in works [4,5,6]
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