LEAST SQUARES WITH EQUALITY CONSTRAINTS

The paper exposes a few useful mathematical facts about ordinary least-squares problems where the vector of unknows x is subject to constraints. They are given as a system of equations. Constraints often follow from a mathematical or physical model. In its simplest form certain prescribed coordinate...

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Vydáno v:Geodezija ir kartografija Ročník 28; číslo 1; s. 3 - 6
Hlavní autoři: Borre, Kai, Borre, K
Médium: Journal Article
Jazyk:angličtina
Vydáno: Taylor & Francis Group 01.01.2002
Témata:
adjustment of geodetic networks
least squares
MATLAB code
ISSN:1392-1541
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Shrnutí:The paper exposes a few useful mathematical facts about ordinary least-squares problems where the vector of unknows x is subject to constraints. They are given as a system of equations. Constraints often follow from a mathematical or physical model. In its simplest form certain prescribed coordinate values shall be left unchanged by the least-squares procedure. By ,,prescribed" we mean that the numerical values have zero variance. A modification of the problem occurs when the variance is close to zero. The concept of soft/hard postulation due to T. Krarup is given. In order to illustrate the use of various formulas the MATLAB code's examples are included that demonstrates the application of the exposed theory.
ISSN:1392-1541
DOI:10.1080/13921541.2002.10552938