Abstract
This paper deals with an extension of the Rayleigh-Ritz method for bracketing eigenvalues of self-adjoint differential operators. The proposed extension uses a simple formula which gives lower bounds of eigenvalues requiring only the Rayleigh-Ritz eigenfunction approximations and a rough lower bound of some higher eigenvalue. The combination of this extended Rayleigh-Ritz method with the widely used exact conformal mapping technique enables one to obtain eigenvalue bounds of the Helmholtz equation defined on the regions with complicated boundary shape. Numerical results concerning the cutoff frequencies of the eccentric annular, eccentric lunar and eccentric inverted lunar waveguide are presented.
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