Error Estimation for Eigenvalues of Unbounded Linear Operators and an Application to Energy Levels in Graphene Quantum Dots

Fredrik Berntsson, Anna Orlof, Johan Thim
2017 Numerical Functional Analysis and Optimization  
The eigenvalue problem for linear differential operators is important since eigenvalues correspond to the possible energy levels of a physical system. It is also important to have good estimates of the error in the computed eigenvalues. In this work we use spline interpolation to construct approximate eigenfunctions of a linear operator by using the corresponding eigenvectors of a discretized approximation of the operator. We show that an error estimate for the approximate eigenvalues can be
more » ... ained by evaluating the residual for an approximate eigenpair. The interpolation scheme is selected in such a way that the residual can be evaluated analytically. In order to demonstrate that the method gives useful error bounds we apply it to a problem originating from the study of graphene quantum dots where the goal was to investigate the change in the spectrum from incorporating electron-electron interactions in the potential.
doi:10.1080/01630563.2017.1279176 fatcat:tztkhxx7prfm3oeh5tqzg7yl5a