with their small computational prefactor and general applicability, remain the default method in most LCAO codes. Even in PW codes, the performance of a dense eigensolver is still crucial, because at some stage of an iterative solver there will be a dense eigenproblem, the size of which scales with the number of valence electrons in the system being simulated. Therefore, any improvement made to a dense eigensolver would benefit the entire electronic structure community, and the broader field of computational science in general.

The ubiquitous adoption of graphics processing units (GPU) in high-performance computing opens up new opportunities to accelerate dense eigensolvers. A GPU device consists of hundreds to thousands of parallel cores operating at a relatively low frequency. These cores are naturally suited for parallel computational tasks, such as vector and matrix operations found in dense linear algebra. On top of that, GPUs typically have a power efficiency superior to traditional CPUs, and therefore play an important role in supercomputing towards the exascale. According to the latest release of the TOP500 list at the time of writing (November 2019) [@top500], five of the top ten machines are GPU-accelerated, including Summit, the world’s fastest computer based on IBM POWER9 CPUs 