APPROXIMATE METHODS FOR COMPUTING THE EIGENELEMENTS OF INTEGRAL AND DIFFERENTIAL LINEAR OPERATORS.

The convergence properties of a number of approximation methods involving an integral operator are reviewed, including the method of degenerate kernels and four classes of projection methods. Also described are the convergence properties of two types of methods involving differential operators, namely the Rayleigh-Galerkin method and the method of approximation by a neighboring operator. Particular attention is paid to determining whether an approximation is collectively compact.