Volume 7, pp. 18-39, 1998.

Harmonic Ritz and Lehmann bounds

Christopher Beattie

Abstract

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 right- and 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.

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Key words

optimal eigenvalue bounds, Lehmann intervals, harmonic Ritz values.

AMS subject classifications

65F15, 49R05.

ETNA articles which cite this article

Vol. 20 (2005), pp. 235-252 Michiel E. Hochstenbach: Generalizations of harmonic and refined Rayleigh-Ritz

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