Volume 7 Number 3 (Jul. 2017)
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IJAPM 2017 Vol.7(3): 148-156 ISSN: 2010-362X
doi: 10.17706/ijapm.2017.7.3.148-156

High Dimensional and Large Span Data Least Square Error: Numerical Stability and Conditionality

Vaclav Skala
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.

General Information

ISSN: 2010-362X
Frequency: Bimonthly (2011-2014); Quarterly (Since 2015)
DOI: 10.17706/IJAPM
Editor-in-Chief: Prof. Haydar Akca
Abstracting/ Indexing: Index Copernicus, EI (INSPEC, IET), Chemical Abstracts Services (CAS), Electronic Journals Library, Nanowerk Database, Google Scholar, EBSCO, and ProQuest
E-mail: ijapm@iap.org
  • Aug 06, 2018 News!

    IJAPM Vol 7, No 1-No 3 have been indexed by EI (Inspec)   [Click]

  • Feb 22, 2019 News!

    The paper published in Vol 9, No 2 has received dois from Crossref

  • Feb 11, 2019 News!

    Vol 9, No 2 has been published with online version     [Click]

  • Dec 21, 2018 News!

    The paper published in Vol 9, No 1 has received dois from Crossref

  • Dec 17, 2018 News!

    Vol 9, No 1 has been published with online version     [Click]

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