Adaptive Projection Subspace Dimension for the Thick-Restart Lanczos Method

The Thick-Restart Lanczos (TRLan) method is an effective method for solving large-scale Hermitian eigenvalue problems. The performance of the method strongly depends on the dimension of the projection subspace used at each restart. In this article, we propose an objective function to quantify the effectiveness of the selection of subspace dimension, and then introduce an adaptive scheme to dynamically select the dimension to optimize the performance. We have developed an open-source software package a --TRLan to include this adaptive scheme in the TRLan method. When applied to calculate the electronic structure of quantum dots, a --TRLan runs up to 2.3x faster than a state-of-the-art preconditioned conjugate gradient eigensolver.