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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Bibliographic Details
Published in:Geodezija ir kartografija Vol. 28; no. 1; pp. 3 - 6
Main Authors: Borre, Kai, Borre, K
Format: Journal Article
Language:English
Published: Taylor & Francis Group 01.01.2002
Subjects:
adjustment of geodetic networks
least squares
MATLAB code
ISSN:1392-1541
Online Access:Get full text
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Summary: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