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Methods for computing lower bounds to eigenvalues of self-adjoint operators. (English) Zbl 0857.65063

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.
Reviewer: A.J.Meir (Auburn)

MSC:

65J10 Numerical solutions to equations with linear operators
35P15 Estimates of eigenvalues in context of PDEs
47A75 Eigenvalue problems for linear operators
47B25 Linear symmetric and selfadjoint operators (unbounded)
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