TY - JOUR
A2 - Sahu, D. R.
AU - Bergamaschi, L.
AU - MartÃnez, A.
PY - 2013
DA - 2013/09/26
TI - Parallel RFSAI-BFGS Preconditioners for Large Symmetric Eigenproblems
SP - 767042
VL - 2013
AB - 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 ofthe 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.
SN - 1110-757X
UR - https://doi.org/10.1155/2013/767042
DO - 10.1155/2013/767042
JF - Journal of Applied Mathematics
PB - Hindawi Publishing Corporation
KW -
ER -