Karhunen-Loève approximation of random fields by generalized fast multipole methods
Journal of Computational Physics - Special issue: Uncertainty quantification in simulation science
Spectral element approximation of Fredholm integral eigenvalue problems
Journal of Computational and Applied Mathematics
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Robust quasi-relative Galerkin discretization error estimates are derived for the eigenvalue problem associated to a nonnegative compact operator $\cal K$ acting in a Hilbert space. Trace discretization error estimates for arbitrarily small positive powers of $\cal K$ are obtained as a consequence. Coupled with bounds on eigenfunction oscillations, the results are then applied to the case of an integral operator with (piecewise) smooth kernel $K$ on a bounded domain and in the context of the $h$ finite element method.