Parallel RFSAI-BFGS Preconditioners for Large Symmetric Eigenproblems
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...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/767042 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832549561928777728 |
|---|---|
| author | L. Bergamaschi A. Martínez |
| author_facet | L. Bergamaschi A. Martínez |
| author_sort | L. Bergamaschi |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-183005a98435467ba93f12d1fe23d53b |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-183005a98435467ba93f12d1fe23d53b2025-02-03T06:10:54ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/767042767042Parallel RFSAI-BFGS Preconditioners for Large Symmetric EigenproblemsL. Bergamaschi0A. Martínez1Department of Civil, Environmental, and Architectural Engineering, University of Padua, Via Trieste 63, 35100 Padova, ItalyDepartment of Mathematics, University of Padua, Via Trieste 63, 35100 Padova, ItalyWe 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.http://dx.doi.org/10.1155/2013/767042 |
| spellingShingle | L. Bergamaschi A. Martínez Parallel RFSAI-BFGS Preconditioners for Large Symmetric Eigenproblems Journal of Applied Mathematics |
| title | Parallel RFSAI-BFGS Preconditioners for Large Symmetric Eigenproblems |
| title_full | Parallel RFSAI-BFGS Preconditioners for Large Symmetric Eigenproblems |
| title_fullStr | Parallel RFSAI-BFGS Preconditioners for Large Symmetric Eigenproblems |
| title_full_unstemmed | Parallel RFSAI-BFGS Preconditioners for Large Symmetric Eigenproblems |
| title_short | Parallel RFSAI-BFGS Preconditioners for Large Symmetric Eigenproblems |
| title_sort | parallel rfsai bfgs preconditioners for large symmetric eigenproblems |
| url | http://dx.doi.org/10.1155/2013/767042 |
| work_keys_str_mv | AT lbergamaschi parallelrfsaibfgspreconditionersforlargesymmetriceigenproblems AT amartinez parallelrfsaibfgspreconditionersforlargesymmetriceigenproblems |