Abstract
Constructing a factor analysis model by the minimal residual method, we propose a solution to the problem of communalities exceeding 1. In order to determine the quantities, an appropriate lemma is proved which allows us to repair the original proof of the Harman theorem on the minimum of the target of the minimal residual method.
Similar content being viewed by others
References
K. Iberla, Factor Analysis (Statistika, Moscow, 1989) [in Russian].
H. H. Harman, Modern Factor Analysis, 2nd ed. (Univ. Chicago, Chicago, 1967; Statistika, Moscow, 1972).
V. V. Gol’tyapin, V. A. Topchii, and V. M. Yakovlev, “A Factor Model of Homeostasis for Diagnostics of Mitral Stenosis of Different Extent,” in Microsensorics (Omsk, 2000), pp. 78–85 [in Russian].
V. V. Gol’tyapin, V. A. Topchii, and V. M. Yakovlev, “A Factor Model in Differential Diagnosis of the Mitral Stenosis,” Med. Fizika, No. 2, 201–212 (2001).
V. V. Gol’tyapin, M. G. Potudanskaya, O. O. Zagarskikh, and N. A. Semikolenova, “Factor Analysis of the Dependence of the ECG Qualitative Characteristics of Healthy People on Anthropological Factors,” Vestnik Aritmologii, No. 35, 196 (2004).
V. M. Verzhibtskii, Fundamentals of Numerical Methods (Vysshaya Shkola,Moscow, 2002) [in Russian].
F. R. Gantmakher, The Theory ofMatrices (Nauka, Moscow, 1988) [in Russian].
V. V. Gol’tyapin, A. G. Lilo, N. A. Morova, N. A. Semikolenova, and V. A. Topchii, “Factor Analysis of the Dependence of the ECG Qualitative Characteristics of Healthy People on Anthropological Factors,” in Measurement. Control. Information Science: Proceedings of the International Conference on Science and Technology (Barnaul, 2000), pp. 127–130.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.V. Gol’tyapin, 2005, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2005, Vol. VIII, No. 3(23), pp. 24–31.
Rights and permissions
About this article
Cite this article
Gol’tyapin, V.V. Computational aspects of the minimal residual method in resolving the heywood case. J. Appl. Ind. Math. 2, 68–73 (2008). https://doi.org/10.1134/S1990478908010080
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1990478908010080