First general algorithms compute spectral measures, point/continuous/singular decompositions, functional calculus, and Radon-Nikodym derivatives for self-adjoint or unitary operators with known column decay, with Solvability Complexity Index classifications.
FEAST for differential eigenvalue problems
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abstract
An operator analogue of the FEAST matrix eigensolver is developed to compute the discrete part of the spectrum of a differential operator in a region of interest in the complex plane. Unbounded search regions are handled with a novel rational filter for the right half-plane. If the differential operator is normal or self-adjoint, then the operator analogue preserves that structure and robustly computes eigenvalues to near machine precision accuracy. The algorithm is particularly adept at computing high-frequency modes of differential operators that possess self-adjoint structure with respect to weighted Hilbert spaces.
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math.SP 1years
2019 1verdicts
CONDITIONAL 1representative citing papers
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Computing Spectral Measures and Spectral Types
First general algorithms compute spectral measures, point/continuous/singular decompositions, functional calculus, and Radon-Nikodym derivatives for self-adjoint or unitary operators with known column decay, with Solvability Complexity Index classifications.