Methods for computing lower bounds to eigenvalues of self-adjoint operators
The authors describe a new approach for computing lower bounds on eigenvalues of selfadjoint operators (in particular differential operators). The derivation of the method depends on intermediate problem formulation but needs no information on eigenvectors of the base problem. The proposed method permits effective use of finite element trial functions; this yields a computational method which involves sparse well-structured matrices. This method may be coupled with a Rayleigh-Ritz method (for computing upper bounds) to obtain bounds on eigenvalues as is illustrated by two computational examples.
scientific article; zbMATH DE number 839153