Robust Successive Computation of Eigenpairs for Nonlinear Eigenvalue Problems
Cedric Effenberger · SIAM Journal on Matrix Analysis and Applications · 2013
Newton-based methods are well-established techniques for solving nonlinear eigenvalue problems. If a larger portion of the spectrum is sought, however, their tendency to reconverge to previously determined eigenpairs is a hindrance. To overcome this limitation, we propose and analyze a deflation strategy for nonlinear eigenvalue problems, based on the concept of minimal invariant pairs. We develop this strategy into a Jacobi--Davidson-type method and discuss its various algorithmic details. Finally, the efficiency of our approach is demonstrated by a sequence of numerical examples.