Stability of Quadratic Projection Methods
  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]. 
Lyonell Boulton, Michael Strauss