Volume 48, pp. 183-201, 2018.

Convergence of integration-based methods for the solution of standard and generalized Hermitian eigenvalue problems

Lukas Krämer and Bruno Lang


Recently, methods based on spectral projection and numerical integration have been proposed in the literature as candidates for reliable high-performance eigenvalue solvers. The key ingredients of this type of eigenvalue solver are a Rayleigh-Ritz process and a routine to compute an approximation to the desired eigenspace. The latter computation can be performed by numerical integration of the resolvent. In this article we investigate the progress of the Rayleigh-Ritz process and the achievable quality of the computed eigenpairs for the case that an upper bound for the normwise difference between the currently used subspace and the desired eigenspace is available. Then, such bounds are derived for the Gauß-Legendre rule and the trapezoidal rule.

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Key words

eigenvalue solver, FEAST, spectral projection method, Rayleigh-Ritz, Gauß-Legendre rule, trapezoidal rule

AMS subject classifications

65F15, 65D30, 30B10

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