Efficient Algorithm for Linear Systems Arising in Solutions of Eigenproblems and Its Application to Electronic-Structure Calculations

We consider an eigenproblem derived from first-principles electronic-structure calculations. Eigensolvers based on a rational filter require solutions of linear systems with multiple shifts and multiple right hand sides for transforming the spectrum. The solutions of the linear systems are the dominant part of the eigensolvers. We derive an efficient algorithm for such linear systems, and develop implementation techniques to reduce time-consuming data copies in the algorithm. Several experiments are performed on the K computer to evaluate the performance of our algorithm.