Successive Approximations by the Rayleigh-Ritz Variation Method

Approximate eigenvalues given by the Rayleigh-Ritz variation method for handling linear differential equations are examined and relations are established between the discrete eigenvalues obtained in successive approximations. These relations should be of use in practical computations. A method for fixing upper bounds to eigenvalues is given and a procedure previously employed by the writer to simplify determinant calculations is adapted for use in the present theory.