Systems of Linear Algebraic Equations with Random Coefficients
Vyacheslav L. Girko · Theory of Probability and Its Applications · 1992
Previous article Next article Systems of Linear Algebraic Equations with Random CoefficientsV. L. GirkoV. L. Girkohttps://doi.org/10.1137/1136030PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] V. V. Voevodin, Calculation Basics of Linear Algebra, Nauka, Moscow, 1977, (In Russian.) Google Scholar[2] A. N. Tikhonov and , V. Ya. Arsenin, The Methods of Solution of Incorrect Problems, Nauka, Moscow, 1986, (In Russian.) Google Scholar[3] D. C. Faddeev and , V. N. Faddeeva, Computational methods of linear algebra, Translated by Robert C. Williams, W. H. Freeman and Co., San Francisco, 1963xi+621 28:1742 Google Scholar[4] J. H. Wilkinson, The algebraic eigenvalue problem, Clarendon Press, Oxford, 1965xviii+662 32:1894 0258.65037 Google Scholar[5] I. N. Molchanov, Computer Methods of Solution of Applied Problems: Algebra, Approximation of Functions, Naukova Dumka, Kiev, 1987, (In Russian.) Google Scholar[6] V. V. Voevodin and , Yu. A. Kuznetsov, Matrices and Calculation, Nauka, Moscow, 1984, (In Russian.) Google Scholar[7] V. L. Girko, On distribution of the solutions of systems of linear equations with random coefficients, Theory Probab. Math. Stat., 2 (1970), 41–44, (In Russian.) Google Scholar[8] V. L. Girko, The law of arctangent, Soviet Math. Dokl., 4 (1980), 7–9, (In Russian.) Google Scholar[9] V. L. Girko, Theory of random determinants, Mathematics and its Applications (Soviet Series), Vol. 45, Kluwer Academic Publishers Group, Dordrecht, 1990xxvi+677 91k:60001 0704.60003 CrossrefGoogle Scholar[10] V. L. Girko, Introduction to general statistical analysis, Theory Probab. Appl., 32 (1987), 229–242, (In Russian.) 10.1137/1132033 0653.62043 LinkGoogle Scholar[11] V. L. Girko, The circular law, Theory Probab. Appl., 29 (1984), 694–000 10.1137/1129095 LinkGoogle Scholar[12] V. L. Girko, G-analysis of observations of large dimension, Vychisl. Prikl. Mat. (Kiev), (1986), 115–121, 128, (In Russian.) 88k:62086 Google Scholar[13] V. L. Girko, $G_{3}$-estimate of the inverse covariance matrix, Vestnik Kievskogo Univ., ser. Model. and Optimiz. of Compex Systems, 60 (1987), 40–44, (In Russian.) Google Scholar[14] V. L. Girko, Multidimensional Statistical Analysis, Vishcha Shkola, Kiev, 1988, (In Russian.) Google Scholar[15] V. L. Girko and , A. S. Babanin, On the estimate of $G_{8}$-solutions of the empirical systems of linear algebraic equations, Theory Probab. Math. Statist., 39 (1988), 29–33, (In Russian.) Google Scholar[16] G. L. Girko, Spectral Theory of Random Matrices, Nauka, Moscow, 1988, (In Russian.) Google Scholar[17] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, Heidelberg, New York, 1966 0148.12601 CrossrefGoogle Scholar[18] F. R. Gantmakher, Theory of Matrices, Nauka, Moscow, 1967, (In Russian.) 0666.15002 Google Scholar[19] V. L. Girko, Consistent $G_{8}$-estimates of the solutions of systems of linear algebraic equations, Theory Probab. Math. Statist., 42, 43 (1990), 14–22, 48–59, (In Russian.) 0748.62016 Google Scholar[20] M. A. Lavrent'ev and , B. V. Shabat, Methods of the Theory of Functions of the Complex Variable, Nauka, Moscow, 1973, (In Russian.) Google Scholar[21] A. I. Markushevich, Theory of Analytic Functions, GTTL, Moscow, Leningrad, 1950, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Concepts of solutions of uncertain equations with intervals, probabilities and fuzzy sets for applied tasks18 October 2016 | Granular Computing, Vol. 2, No. 3 Cross Ref Comparison of formulations of applied tasks with intervals, fuzzy sets and probability approaches Cross Ref Unimprovable solution to systems of empirical linear algebraic equationsStatistics & Probability Letters, Vol. 60, No. 1 Cross Ref Volume 36, Issue 2| 1992Theory of Probability & Its Applications History Submitted:12 September 1988Published online:17 July 2006 InformationCopyright © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1136030Article page range:pp. 261-271ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics