doi: 10.17706/ijapm.2017.7.3.148-156
High Dimensional and Large Span Data Least Square Error: Numerical Stability and Conditionality
Vaclav Skala
- Department of Computer Science and Engineering, Faculty of Applied Sciences, University of West Bohemia, CZ 306 14 Plzen, Czech Republic
Abstract
The Least Square Error (LSE) is widely used method in many engineering and computational problems solution. The LSE method is simple from the “formulation” point of view, offers a simple solution. However, it might lead to wrong or incorrect conclusions, especially if high dimensional or large span data are to be processed or if some variables have significantly smaller influence than the other does, e.g. inconvenient selection of measuring units. In this paper, we analyze influence of row and column “normalization” inspired by the Gershgorin’s theorem. The approach has been experimentally verified on a LSE application for high dimensional and large span data. The proposed approach was tested also on Hilbert’s matrix inversion for conditional number change analysis.
Keywords
- Least square error
- conditionality
- robustness
- Gershgorin’s theorem
- numerical stability
How to Cite
Vaclav Skala, "High Dimensional and Large Span Data Least Square Error: Numerical Stability and Conditionality," International Journal of Applied Physics and Mathematics, vol. 7, no. 3, pp. 148-156, 2017. https://doi.org/ 10.17706/ijapm.2017.7.3.148-156
Copyright & License
Copyright © 2017 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).