METHODS FOR COMPUTING LOWER BOUNDS TO EIGENVALUES OF SELF-ADJOINT OPERATORS

New approaches for computing tight lower bounds to the eigenvalues of a class of semibounded self-adjoint operators are presented that requi re comparatively little a priori spectral information and permit the e ffective use of (among others) finite-element trial functions, A varia nt of the method of intermediate problems making use of operator decom positions having the form TT is reviewed and then developed into a ne w framework based on recent inertia results in the Weinstein-Aronszajn theory, This framework provides greater flexibility in analysis and p ermits the formulation of a final computational task involving sparse, well-structured matrices. Although our derivation is based on an inte rmediate problem formulation, our results may be specialized to obtain either the Temple-Lehmann method or Weinberger's matrix method.