An a priori bound for eigenvalue computation by AMLS

Based on Schur complements and modal approximations of submatrices on several levels AMLS constructs a projected eigenproblem which yields good approximations of eigenvalues at the lower end of the spectrum. Rewriting the original problem as a rational eigenproblem of the same dimension as the projected problem, and taking advantage of a minmax characterization for the rational eigenproblem we derive a bound for the AMLS approximation of eigenvalues. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)