Summary.
New approaches for computing tight lower bounds to the eigenvalues of a class of semibounded self-adjoint operators are presented that require comparatively little a priori spectral information and permit the effective use of (among others) finite-element trial functions. A variant of the method of intermediate problems making use of operator decompositions having the form\(T^*T\) is reviewed and then developed into a new framework based on recent inertia results in the Weinstein-Aronszajn theory. This framework provides greater flexibility in analysis and permits the formulation of a final computational task involving sparse, well-structured matrices. Although our derivation is based on an intermediate problem formulation, our results may be specialized to obtain either the Temple-Lehmann method or Weinberger's matrix method.
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Received December 12, 1992 / Revised version received October 5, 1994
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Beattie, C., Goerisch, F. Methods for computing lower bounds to eigenvalues of self-adjoint operators . Numer. Math. 72, 143–172 (1995). https://doi.org/10.1007/s002110050164
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DOI: https://doi.org/10.1007/s002110050164