Performance of block Jacobi-Davidson solvers

Abstract

Jacobi-Davidson methods can efficiently compute a few eigenpairs of a large sparse matrix. Block variants of Jacobi-Davidson are known to be more robust than the standard algorithm, but they are usually avoided as the total number of floating point operations increases. We present the implementation of a block Jacobi-Davidson solver and show by detailed performance engineering and numerical experiments that the increase in operations is typically more than compensated by performance gains on modern architectures, giving a method that is both more efficient and robust than its single vector counterpart.