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In Density Functional Theory simulations based on the LAPW method, eachself-consistent field cycle comprises dozens of large dense generalizedeigenproblems. In contrast to real-space methods, eigenpairs solving forproblems at distinct cycles have either been believed to be independent or atmost very loosely connected. In a recent study [7], it was demonstrated that,contrary to belief, successive eigenproblems in a sequence are stronglycorrelated with one another. In particular, by monitoring the subspace anglesbetween eigenvectors of successive eigenproblems, it was shown that theseangles decrease noticeably after the first few iterations and become close tocollinear. This last result suggests that we can manipulate the eigenvectors,solving for a specific eigenproblem in a sequence, as an approximate solutionfor the following eigenproblem. In this work we present results that are inline with this intuition. We provide numerical examples where opportunelyselected block iterative eigensolvers benefit from the reuse of eigenvectors byachieving a substantial speed-up. The results presented will eventually openthe way to a widespread use of block iterative eigensolvers in ab initioelectronic structure codes based on the LAPW approach.

Block Iterative Eigensolvers for Sequences of Correlated Eigenvalue Problems