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A certified strategy for determining sharp intervals of enclosure for the eigenvalues of matrix differential operators with singular coefficients is examined. The strategy relies on computing the second order spectrum relative to subspaces of continuous piecewise linear functions. For smooth perturbations of the angular Kerr-Newman Dirac operator, explicit rates of convergence due to regularity of the eigenfunctions are established. Existing benchmarks are validated and sharpened by several orders of magnitude in the unperturbed setting.
This paper is concerned with methods for numerical computation of eigenvalue enclosures. We examine in close detail the equivalence between an extension of the Lehmann-Maehly-Goerisch method developed a few years ago by Zimmermann and Mertins, and a
We propose employing the extension of the Lehmann-Maehly-Goerisch method developed by Zimmermann and Mertins, as a highly effective tool for the pollution-free finite element computation of the eigenfrequencies of the resonant cavity problem on a bou
We prove new spectral enclosures for the non-real spectrum of a class of $2times2$ block operator matrices with self-adjoint operators $A$ and $D$ on the diagonal and operators $B$ and $-B^*$ as off-diagonal entries. One of our main results resembles
We exposit the eigenvalue distribution of the lattice Dirac operator in Quantum Chromodynamics with two colors (i.e. two-color QCD). We explicitly calculate all the eigenvalues in the presence of finite quark chemical potential mu for a given gauge c
We use Heun type solutions given in cite{Suzuki} for the radial Teukolsky equation, written in the background metric of the Kerr-Newman-de Sitter geometry, to calculate the quasinormal frequencies for polynomial solutions and the reflection coefficie