A Hierarchical Method for obtaining Eigenvalue Enclusures

Details A Hierarchical Method for obtaining Eigenvalue Enclusures A Hierarchical Method for obtaining Eigenvalue Enclusures

1998-03-17

arxiv.org/abs/math/9803075v2

Mathematics

Spectral Theory

Scientific paper

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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