UDC: 
DOI: 
10.22389/0016-7126-2023-991-1-20-28
1 Shevshenko G.G.
2 Bryn M.Ya.
3 Naumova N.A.
Year: 
№: 
991
Pages: 
20-28

Kuban State Technological University

1, 
3, 

Petersburg State Transport University

2, 
Abstract:
The authors consider the possibility of using the search method to perform pseudo-rotation of matrices at equalizing free geodetic networks. Two methods of pseudo-circulation of matrices are proposed: the first one is based on the calculation of the pseudo-inverse matrix through the execution of the conversion procedure as an intermediate step carried out by the search method; the second enables obtaining the required matrix directly through the search method, without their intermediate calculations. A theoretical justification was carried out with developing a step-by-step algorithm for each of the proposed means. The techniques were tested on a test example. The correctness of the obtained pseudo-circulation results is confirmed by the coincidence of the final calculations performed through the classical pseudo-circulation method, the Greville. The equalization of a free geodesic polygon is performed with the search method using both ones for pseudo-circulation of the unknowns’ N normal equations coefficients matrix. The correctness of the final results of the equalization is confirmed by the coincidence of similar calculations performed through the parametric method and the outcome of pseudo-circulation N performed using skeletal decomposition.
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Citation:
Shevshenko G.G., 
Bryn M.Ya., 
Naumova N.A., 
(2023) Pseudoinversion of matrices through the search method of nonlinear programming in the equalization of free geodesic networks. Geodesy and cartography = Geodezia i Kartografia, 84(1), pp. 20-28. (In Russian). DOI: 10.22389/0016-7126-2023-991-1-20-28
Publication History
Received: 25.10.2022
Accepted: 28.12.2022
Published: 20.02.2023

Content

2023 January DOI:
10.22389/0016-7126-2023-991-1

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