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Rellich F. Perturbation theory of eigenvalue problems

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Rellich F. Perturbation theory of eigenvalue problems
New York: Gordon and Breach, 1969. — 140 p.
Perturbation methods attempt to solve a given problem by approximating it by simpler problems whose solutions are more or less explicitly known.
In eigenvalue problems the perturbation method yields numerical results comparatively quickly provided you are satisfied with approximations of low
order. However, even in problems which appear to be very simple, it might be difficult to ascertain whether or not the method applied would converge
if continued ad infinitum or to estimate the error incurred by stopping at a certain order of approximation. Sometimes the method obviously does not
converge-at least not in the usual sense; then there is the problem of trying to interpret the results computed, if they have any significance at all. The
following examples illustrate the mathematical problems involved in these questions.
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