Sharp eigenvalue enclosures for the perturbed angular Kerr–Newman Dirac operator

Lyonell Boulton, Monika Winklmeier

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We examine a certified strategy for determining sharp intervals of enclosure for the eigenvalues of matrix differential operators with singular coefficients. 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 linked to regularity of the eigenfunctions are established. Numerical tests which validate and sharpen by several orders of magnitude the existing benchmarks are also included.
Original languageEnglish
Article number20150232
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2182
Early online date30 Sept 2015
Publication statusPublished - Oct 2015


  • Angular Kerr-Newman Dirac operator
  • Computation of upper and lower bounds for eigenvalues
  • Numerical approximation of eigenvalues
  • Projection methods

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)


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