  The exact computation of asymptotic quasinormal frequencies is a technical
problem which involves the analytic continuation of a Schrodinger-like equation
to the complex plane and then performing a method of monodromy matching at the
several poles in the plane. While this method was successfully used in
asymptotically flat spacetime, as applied to both the Schwarzschild and
Reissner-Nordstrom solutions, its extension to non-asymptotically flat
spacetimes has not been achieved yet. In this work it is shown how to extend
the method to this case, with the explicit analysis of Schwarzschild de Sitter
and large Schwarzschild Anti-de Sitter black holes, both in four dimensions. We
obtain, for the first time, analytic expressions for the asymptotic quasinormal
frequencies of these black hole spacetimes, and our results match previous
numerical calculations with great accuracy. We also list some results
concerning the general classification of asymptotic quasinormal frequencies in
d-dimensional spacetimes.
