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A recursion method for statistical estimation of eigenvalues and eigenvectors of matrices. (English. Russian original) Zbl 0704.62070

Sov. J. Comput. Syst. Sci. 27, No. 2, 60-64 (1989); translation from Izv. Akad. Nauk SSSR, Tekh. Kibern. 1988, No. 6, 39-44 (1988).
This paper presents a recursive method for stochastic approximation of the maximum eigenvalue of the mean value of a random symmetric matrix. The method is applicable not just to positive-definite matrices but also to matrices of a much more general kind.
A series of results from the literature is surveyed in the introduction. The following paragraph presents recursion estimates of the maximum and minimum eigenvalues and the corresponding eigenvectors of the covariance matrix from sample data. Here the authors proved two theorems which make possible a relatively simple analysis of convergence of the proposed recursion method. A general recursion scheme is given in the last part of this paper.
The paper contains clear and efficient demonstrations which can be used for teaching purpose. The immediate applicability of this paper makes it both useful and interesting.
Reviewer: P.Cotae

MSC:

62L20 Stochastic approximation
60G35 Signal detection and filtering (aspects of stochastic processes)
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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