Abstract A parallel algorithm based on the multidimensional minimization of the Rayleigh quotient is proposed to evaluate the 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) and by a number of block preconditioners. The resulting code obtains a high level of parallel efficiency and proves to be comparable with the PARPACK package on a set of large matrices arising from various discretizations of PDEs of elliptic/parabolic type.
Parallel preconditioned conjugate gradient optimization of the Rayleigh quotient for the solution of sparse eigenproblems / Bergamaschi, L.; Martinez, A.; Pini, G.. - In: APPLIED MATHEMATICS AND COMPUTATION. - ISSN 0096-3003. - ELETTRONICO. - 175:(2006), pp. 1694-1715. [10.1016/j.amc.2005.09.015]
Parallel preconditioned conjugate gradient optimization of the Rayleigh quotient for the solution of sparse eigenproblems
MARTINEZ A.;
2006-01-01
Abstract
Abstract A parallel algorithm based on the multidimensional minimization of the Rayleigh quotient is proposed to evaluate the 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) and by a number of block preconditioners. The resulting code obtains a high level of parallel efficiency and proves to be comparable with the PARPACK package on a set of large matrices arising from various discretizations of PDEs of elliptic/parabolic type.Pubblicazioni consigliate
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