Adaptive choice of projectors in projection based eigensolvers
Martin Galgon, Bruno Lang · 2015
We present a general framework for algorithms for the solution of Hermitian eigenvalue problems, where eigenvalues in a given interval are sought. One instance of this framework is Polizzi’s FEAST algorithm [E. Polizzi: Density-matrix-based algorithm for solving eigenvalue problems. Phys. Rev. B 2009; 79:115112], which is based on numerical integration. Another instance is based on polynomial approximation. We propose adaptive strategies for the choice of the polynomial degree and tolerance of the linear solver, respectively. Numerical experiments reveal that these strategies are able to improve the robustness of the resulting methods, while at the same time achieving near-to-optimum eciency.