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.

Index Terms—Least square error, conditionality, robustness, Gershgorin’s theorem, numerical stability.

Vaclav Skala is with Department of Computer Science and Engineering, Faculty of Applied Sciences, University of West Bohemia, CZ 306 14 Plzen, Czech Republic (email: skala@kiv.zcu.cz).

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.