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.
Parallel solution of sparse eigenproblems by simultaneous Rayleigh quotient optimization with FSAI preconditioning
BERGAMASCHI, LUCA;MARTINEZ CALOMARDO, ANGELES;PINI, GIORGIO
2004
Abstract
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.
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