Geodesic
Harmonic Ritz and Lehmann bounds
Electronic transactions on numerical analysis, Tome 7 (1998), pp. 18-39
This article reviews a variety of results related to optimal bounds for matrix eigenvalues - some results presented here are well-known; others are less known; and a few are new. The focus rests especially on Ritz and harmonic Ritz values, and rightand left-definite variants of Lehmann's optimal bounds. Two new computationally advantageous reformulations of left-definite Lehmann bounds are introduced, together with a discussion indicating why they might be preferable to the cheaper right-definite bounds.
Classification : 65F15, 49R05
Keywords: optimal eigenvalue bounds, lehmann intervals, harmonic ritz values 
@article{ETNA_1998__7__a11,
     author = {Beattie,  Christopher},
     title = {Harmonic {Ritz} and {Lehmann} bounds},
     journal = {Electronic transactions on numerical analysis},
     pages = {18--39},
     year = {1998},
     volume = {7},
     zbl = {0918.65027},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_1998__7__a11/}
}
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%0 Journal Article
%A Beattie,  Christopher
%T Harmonic Ritz and Lehmann bounds
%J Electronic transactions on numerical analysis
%D 1998
%P 18-39
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%U http://geodesic.mathdoc.fr/item/ETNA_1998__7__a11/
%G en
%F ETNA_1998__7__a11
Beattie,  Christopher. Harmonic Ritz and Lehmann bounds. Electronic transactions on numerical analysis, Tome 7 (1998), pp. 18-39. http://geodesic.mathdoc.fr/item/ETNA_1998__7__a11/