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We show the strongly stable convergence of some non-collectively-compact approximations of compact operators. Special attention is devoted to Anselone's singularity subtraction discretization of certain singular integral operators. Numerical experiments are provided.

In several applications needing the numerical computation of eigenvalues and eigenvectors we deal with strongly quasi-diagonal matrices. An iterative explicit method for this kind of problem is proposed here. Its convergence is proved by means of an argument based on the perturbed fixed slope method. Numerical experiments complete this work.