The equalization of geodetic and leveling networks often leads to systems of linear equations, the determinants of which are close to or equal to zero. Obviously, in this case, the system of equations for corrections to the coordinates of observation points is special, and when the positions of the points are close, the values of the corrections are found rather roughly.
The paper considers a stable method for solving ill-conditioned linear systems by the pseudo inverse matrix method. This approach makes it possible to carry out the equalization without preliminary study of the leveling scheme and provides for obtaining correction values that are resistant to calculation errors. A specific example illustrates the effectiveness of the given methodology, which makes it possible to recommend it for other equalization problems in geodesy, in which the determinant of the system is equal to or close to zero.
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