Lord Rayleigh suggested, in 1894, the inclusion of an unknown exponential parameter in the coordinate functions which are used in connection with his now classical method. Since the calculated eigenvalues constitute upper bounds, one is able to optimize the results by minimizing the eigenvalues with respect to the undetermined exponential parameter. This review presents some recent applications of the approach to finite element algorithmic procedures and an extension of the Kantorovich method made possible by Rayleigh’s optimization concept.

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