Lower Bounds to the Eigenvalues in One-Dimensional Problems by a Shift in the Weight Function

[+] Author and Article Information
D. Pnueli

Department of Mechanical Engineering, Technion, Haifa, Israel

J. Appl. Mech 37(2), 267-270 (Jun 01, 1970) (4 pages) doi:10.1115/1.3408499 History: Received May 23, 1969; Revised October 14, 1969; Online April 06, 2010


A method is presented to obtain both upper and lower bound to eigenvalues when a variational formulation of the problem exists. The method consists of a systematic shift in the weight function. A detailed procedure is offered for one-dimensional problems, which makes improvement of the bounds possible, and which involves the same order of detailed computation as the Rayleigh-Ritz method. The main contribution of this method is that it yields the “other bound;” i.e., the one which cannot be obtained by the Rayleigh-Ritz method.

Copyright © 1970 by ASME
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