Geodesy
UDC: 
DOI: 
10.30533/0536-101X-2019-63-2-145-151
Year: 
2019
Tom: 
63
#: 
2
366
Pages: 
145-151
Abstract:
Necessary information on the Householder reflection is provided. This reflection allows to transform an arbitrary vector in strict accordance with the law of optical reflection. The matrix description of this method sets the Householder transformation which allows, in particular, to reduce the arbitrary rectangular matrix of full rank to the trapezoidal and then the upper triangular form. On the basis of the specified procedure the simple and efficient algorithm of the solution of the standard least squares problem arising, in particular, in geodetic practice is described in article. In this work the new algorithm of adjustment by the correlate method is constructed. This method is widely used, in particular, at mathematical processing of different geodetic constructions. Consecutive Householder reflection of columns of the transposed matrix of the conditional equations’ coefficients is similar to its well-known QR decomposition in linear algebra. But at the same time there is no need to carry out such decomposition practically. As the output of the specified reflections we receive an upper triangular matrix which can be treated as a root square of the correlate normal equations’ matrix. It disposes of the difficulty of setting up and solving the normal equations that usually makes the main part of a traditional algorithm. Also it considerably simplifies obtaining correlates and estimation of a varience-covarience matrix of results of adjustment.
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Publication History
Received: 04.12.2018
Accepted: 04.04.2019
Published: 24.04.2019

Content

2019 issue 2
DOI 10.30533/0536-101X-2019-63-2