  In this paper we discuss the stability of an alternative pollution-free
procedure for computing spectra. The main difference with the Galerkin method
lies in the fact that it gives rise to a weak approximate problem which is
quadratic in the spectral parameter, instead of linear. Previous accounts on
this new procedure can be found in Levitin and Shargorodsky (2002)
[math.SP/0212087] and Boulton (2006) [math.SP/0503126].
