Parallel solution of sparse eigenproblems by simultaneous Rayleigh quotient optimization with FSAI preconditioning

A parallel algorithm based on the S-dimensional minimization of the Rayleigh quotient is proposed to evaluate the s ~ S/2 leftmost eigenpairs of the generalized symmetric positive definite eigenproblem. The minimization is performed via a conjugate gradient-like procedure accelerated by a factorized approximate inverse preconditioner (FSAI). The resulting code attains a high level of parallel efficiency and reveals comparable with the PARPACK package on a set of large matrices.