Abstract
The problem of minimizing the Rayleigh quotient in the presence of constraints is considered. A method for obtaining two-sided bounds for the smallest eigenvalue is suggested. Bibliography: 4 titles.
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REFERENCES
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Yu. Sh. Abramov, Variational Methods in the Theory of Operator Pencils. Spectral Optimization [in Russian], The Leningrad State University, Leningrad (1983).
V. N. Glushkov and A. Ya. Tsaune, “Unconditional minimization in eigenvalue problems with additional conditions," Zh. Vychisl. Mat. Mat. Fiz., 25, No. 2, 298–301 (1985).
D. K. Faddeev and V. N. Faddeeva, Computational Methods of Linear Algebra [in Russian], Fizmatgiz, Moscow (1963).
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Savinov, G.V. Two-Sided Bounds for the Smallest Eigenvalue of a Positive-Definite Matrix in the Presence of Constraints. Journal of Mathematical Sciences 114, 1857–1859 (2003). https://doi.org/10.1023/A:1022466822055
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DOI: https://doi.org/10.1023/A:1022466822055