In order to determine the vector of the coordinates of the free geodetic networks by the least square adjustment, it is necessary to solve a singular system of linear equations and to find the inverse of a singular matrix. It is well known that there is a unique inverse of a regular square matrix. The main question is how to find the inverse of a singular matrix. This paper describes the traditional approach to the solving of the singular problem in opposition to the singular value decomposition (SVD). To exemplify, a free two-dimensional (2D) geodetic network was used to obtain and compare both the traditional and the SVD solutions. The analysis of the two approaches to the problem solving is of particular interest to this work. The advantages of the SVD approach are summarized and suggested to be used more frequently.
Keywords:
geodetic networks / least square method / linear systems / singular value decomposition
TY - JOUR
AU - Božić, Branko
AU - Ristić, Kornelija
AU - Pejić, Marko
PY - 2014
UR - http://grafar.grf.bg.ac.rs/handle/123456789/612
AB - In order to determine the vector of the coordinates of the free geodetic networks by the least square adjustment, it is necessary to solve a singular system of linear equations and to find the inverse of a singular matrix. It is well known that there is a unique inverse of a regular square matrix. The main question is how to find the inverse of a singular matrix. This paper describes the traditional approach to the solving of the singular problem in opposition to the singular value decomposition (SVD). To exemplify, a free two-dimensional (2D) geodetic network was used to obtain and compare both the traditional and the SVD solutions. The analysis of the two approaches to the problem solving is of particular interest to this work. The advantages of the SVD approach are summarized and suggested to be used more frequently.
PB - Faculty of Mechanical Engineering in Slavonski Brod, Faculty of Electrical Engineering in Osijek, Faculty of Civil Engineering in Osijek
T2 - Tehnički vjesnik / Technical Gazette
T1 - Parameter estimation and accuracy analysis of the free geodetic network adjustment using singular value decomposition
EP - 456
IS - 2
SP - 451
VL - 21
ER -
@article{
author = "Božić, Branko and Ristić, Kornelija and Pejić, Marko",
year = "2014",
url = "http://grafar.grf.bg.ac.rs/handle/123456789/612",
abstract = "In order to determine the vector of the coordinates of the free geodetic networks by the least square adjustment, it is necessary to solve a singular system of linear equations and to find the inverse of a singular matrix. It is well known that there is a unique inverse of a regular square matrix. The main question is how to find the inverse of a singular matrix. This paper describes the traditional approach to the solving of the singular problem in opposition to the singular value decomposition (SVD). To exemplify, a free two-dimensional (2D) geodetic network was used to obtain and compare both the traditional and the SVD solutions. The analysis of the two approaches to the problem solving is of particular interest to this work. The advantages of the SVD approach are summarized and suggested to be used more frequently.",
publisher = "Faculty of Mechanical Engineering in Slavonski Brod, Faculty of Electrical Engineering in Osijek, Faculty of Civil Engineering in Osijek",
journal = "Tehnički vjesnik / Technical Gazette",
title = "Parameter estimation and accuracy analysis of the free geodetic network adjustment using singular value decomposition",
pages = "456-451",
number = "2",
volume = "21"
}
Božić, B., Ristić, K.,& Pejić, M. (2014). Parameter estimation and accuracy analysis of the free geodetic network adjustment using singular value decomposition.
Tehnički vjesnik / Technical Gazette
Faculty of Mechanical Engineering in Slavonski Brod, Faculty of Electrical Engineering in Osijek, Faculty of Civil Engineering in Osijek., 21(2), 451-456.
Božić B, Ristić K, Pejić M. Parameter estimation and accuracy analysis of the free geodetic network adjustment using singular value decomposition. Tehnički vjesnik / Technical Gazette. 2014;21(2):451-456
Božić Branko, Ristić Kornelija, Pejić Marko, "Parameter estimation and accuracy analysis of the free geodetic network adjustment using singular value decomposition" Tehnički vjesnik / Technical Gazette, 21, no. 2 (2014):451-456
