Applying Newton’s second order optimization method to define transition keys between planar coordinate systems

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.

[1]  N N Eliseeva,et al.  Application of an evolutionary algorithm to a software suite for determining degrees of tilt in cylindrical structures based on terrestrial laser scanning data , 2019, IOP Conference Series: Materials Science and Engineering.

[2]  N. N. Eliseeva,et al.  The application of search methods for solving optimization problems , 2019, Topical Issues of Rational Use of Natural Resources 2019.

[3]  S. Bian,et al.  An optimized method to transform the Cartesian to geodetic coordinates on a triaxial ellipsoid , 2019, Studia Geophysica et Geodaetica.

[4]  A Sholomitskii,et al.  Design and Preliminary Calculation of the Accuracy of Special Geodetic and Mine Surveying Networks , 2019, IOP Conference Series: Earth and Environmental Science.

[5]  S. Kryltcov,et al.  APPLICATION OF AN ACTIVE RECTIFIER USED TO MITIGATE CURRENTS DISTORTION IN 6-10 KV DISTRIBUTION GRIDS , 2019, Journal of Mining Institute.

[6]  Hong Hui Tan,et al.  Review of second-order optimization techniques in artificial neural networks backpropagation , 2019, IOP Conference Series: Materials Science and Engineering.

[7]  A. S. Vasil'ev,et al.  SPECIAL STRATEGY OF TREATMENT OF DIFFICULTY-PROFILE CONICAL SCREW SURFACES OF SINGLE-SCREW COMPRESSORS WORKING BODIES , 2019, Journal of Mining Institute.

[8]  V. Valkov,et al.  Satellite-based techniques for monitoring of bridge deformations , 2018, Journal of Physics: Conference Series.

[9]  O. Akyilmaz,et al.  Total Least Squares Solution of Coordinate Transformation , 2007 .

[10]  Boštjan Kovačič,et al.  Non-contact monitoring for assessing potential bridge damages , 2020, E3S Web of Conferences.

[11]  M. G. Mustafin,et al.  Monitoring of Quarry Slope Deformations with the Use of Satellite Positioning Technology and Unmanned Aerial Vehicles , 2017 .

[12]  M. G. Mustafin,et al.  Monitoring of Deformation Processes in Buildings and Structures in Metropolises , 2017 .

[13]  Shuqiang Xue,et al.  A New Newton-Type Iterative Formula for Over-Determined Distance Equations , 2014 .