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Parallel RFSAI-BFGS Preconditioners for Large Symmetric Eigenproblems
Joint Authors
Source
Journal of Applied Mathematics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-09-26
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
We propose a parallel preconditioner for the Newton method in the computation of the leftmost eigenpairs of large and sparse symmetric positive definite matrices.
A sequence of preconditioners starting from an enhanced approximate inverse RFSAI (Bergamaschi and Martínez, 2012) and enriched by a BFGS-like update formula is proposed to accelerate the preconditioned conjugate gradient solution of the linearized Newton system to solve Au=q(u)u, q(u) being the Rayleigh quotient.
In a previous work (Bergamaschi and Martínez, 2013) the sequence of preconditioned Jacobians is proven to remain close to the identity matrix if the initial preconditioned Jacobian is so.
Numerical results onto matrices arising from various realistic problems with size up to 1.5 million unknowns account for the efficiency and the scalability of the proposed low rank update of the RFSAI preconditioner.
The overall RFSAI-BFGS preconditioned Newton algorithm has shown comparable efficiencies with a well-established eigenvalue solver on all the test problems.
American Psychological Association (APA)
Bergamaschi, L.& Martínez, A.. 2013. Parallel RFSAI-BFGS Preconditioners for Large Symmetric Eigenproblems. Journal of Applied Mathematics،Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-497123
Modern Language Association (MLA)
Bergamaschi, L.& Martínez, A.. Parallel RFSAI-BFGS Preconditioners for Large Symmetric Eigenproblems. Journal of Applied Mathematics No. 2013 (2013), pp.1-10.
https://search.emarefa.net/detail/BIM-497123
American Medical Association (AMA)
Bergamaschi, L.& Martínez, A.. Parallel RFSAI-BFGS Preconditioners for Large Symmetric Eigenproblems. Journal of Applied Mathematics. 2013. Vol. 2013, no. 2013, pp.1-10.
https://search.emarefa.net/detail/BIM-497123
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-497123