A Hierarchical Method for obtaining Eigenvalue Enclusures

E B Davies

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A Hierarchical Method for obtaining Eigenvalue Enclusures

E B Davies

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Abstract

We propose a method for obtaining rigorous and accurate upper and lower bounds on the eigenvalues of ordinary and partial differential operators in bounded regions of Euclidean space. It uses a boundary condition homotopy method starting from a decomposition of the region into several simpler regions for which the eigenvalues can already be computed accurately. Several numerical examples are presented.

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E B Davies. 1998-03-27. A Hierarchical Method for obtaining Eigenvalue Enclusures. https://arxiv.org/abs/math/9803075

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