| Abstract: |
| Recently, there has been interest in high-precision approximations of
the fundamental eigenvalue of the Laplace-Beltrami operator on
spherical triangles for combinatorial purposes. We present
computations of improved and rigorous enclosures to these eigenvalues.
This is achieved by applying the method of particular solutions in
high precision, the enclosure being obtained by a combination of
interval arithmetic and Taylor models. The index of the eigenvalue can
be certified by exploiting the monotonicity of the eigenvalue with
respect to the domain. The classically troublesome case of singular
corners we handle by combining expansions from all singular corners
and an expansion from an interior point. |
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