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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 37 | Number 3 | Year 2016 | Article Id. IJMTT-V37P526 | DOI : https://doi.org/10.14445/22315373/IJMTT-V37P526

Optimisation of Least Squares Algorithm: A Study of Frame Based Programming Techniques in Horizontal Networks


C. P. E. Agbachi
Abstract

Least squares estimation, a regression technique based on minimisation of residuals, has been invaluable in bringing the best fit solutions to parameters in science and engineering. However, in dynamic environments such as in Geomatic Engineering, formation of these equations can be very challenging. And these constraints are ported and apparent in most program models, requiring users at ease with the subject matter. This paper reviews the methods of least squares approximation and examines a one-step automated approach, through the instrumentality of frames, object oriented programming.

Keywords
Traverse, Observation Equations, Linear Models, Covariance, Semantic Nets.
References

[1] Joe D. Hoffman, “Numerical Methods for Engineers and Scientists”,Marcel Dekker,2ndEdition, 2001.
[2] Hervé Abdi, “Theory of Least Squares”,In N.J. Salkind (Ed.): Encyclopedia of Measurement and Statistics. Thousand Oaks (CA): Sage 2007.
[3] Steven C. Chapra, “Applied Numerical Methods with MATLAB® for Engineers and Scientists,” 3rd Edition, McGraw-Hill 2012.
[4] M. A. R. Cooper, “Control Surveys in Civil Engineering”, Collins 1987.
[5] D. E. Wells, E. J. Krakiwsky, “The Method of Least Squares”, Lecture Notes 18, Department of Geodesy and Geomatics Engineering,UNB, 1997.
[6] R. E. Deakin, “Notes on Least Squares 7”, Geospatial Science, RMIT University, 2005.
[7] B. D. F. Methley, “Computational Models in Surveying and Photogrammetry”, Blackie 1986.
[8] C. P. E. Agbachi, “Design and Application of Concurrent Double Key Survey Data Structures”, IJCTT, Volume 36 Number 3 - June 2016.
[9] J.E. Akin, “Object Oriented Programming Concepts”, ©2001 J.E Akin, https://www.clear.rice.edu/../oop3.pdf.
[10] John A. Bullinaria, “IAI : Semantic Networks and Frames,” © John A. Bullinaria, 2005.
[11] Matthew Huntbach, “Notes on Semantic Nets and Frames”,Dept of Computer Science, Queen Mary and Westfield College, London.
[12] Motaz Abdel Azeem, ”Start Programming Using Object Pascal”, http://www.lazarus-ide.org/
[13] Marco Cantù, “Object Pascal Handbook”, © 1995-2016 Marco Cantù. http://www.marcocantu.com/objectpascal

Citation :

C. P. E. Agbachi, "Optimisation of Least Squares Algorithm: A Study of Frame Based Programming Techniques in Horizontal Networks," International Journal of Mathematics Trends and Technology (IJMTT), vol. 37, no. 3, pp. 190-198, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V37P526

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