Toward Restarting Strategies Tuning for a Krylov Eigenvalue Solver

rylov eigensolvers are used in many scientific fields, such as nuclear physics, page ranking, oil and gas exploration, etc. In this paper, we focus on the ERAM Krylov eigensolver whose convergence is strongly correlated to the Krylov subspace size and the restarting vector \(v_0\), a unit norm vector. We focus on computing the restarting vector \(v_0\) to accelerate the ERAM convergence. First, we study different restarting strategies and compare their efficiency. Then, we mix these restarting strategies and show the considerable ERAM convergence improvement. Mixing the restarting strategies optimizes the “numerical efficiency” versus “execution time” ratio as we do not introduce neither additionnal computation nor communications.