Non-variational computation of the eigenstates of Dirac operators with radially symmetric potentials

Author:

Boulton Lyonell,Boussaid Nabile

Abstract

AbstractWe discuss a novel strategy for computing the eigenvalues and eigenfunctions of the relativistic Dirac operator with a radially symmetric potential. The virtues of this strategy lie in the fact that it avoids completely the phenomenon of spectral pollution and it always provides two-sided estimates for the eigenvalues with explicit error bounds on both eigenvalues and eigenfunctions. We also discuss convergence rates of the method and illustrate our results with various numerical experiments.

Publisher

Wiley

Subject

Computational Theory and Mathematics,General Mathematics

Cited by 10 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. On the convergence of the quadratic method;IMA Journal of Numerical Analysis;2015-07-14

2. Spectral Enclosure and Superconvergence for Eigenvalues in Gaps;Integral Equations and Operator Theory;2015-07-01

3. A new approach to spectral approximation;Journal of Functional Analysis;2014-10

4. Non-consistent approximations of self-adjoint eigenproblems: application to the supercell method;Numerische Mathematik;2014-04-16

5. The second order spectrum and optimal convergence;Mathematics of Computation;2013-04-09

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