Factorized sparse approximate inverse preconditionings I: theory
SIAM Journal on Matrix Analysis and Applications
A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
Parallel Preconditioning with Sparse Approximate Inverses
SIAM Journal on Scientific Computing
MPI-The Complete Reference, Volume 1: The MPI Core
MPI-The Complete Reference, Volume 1: The MPI Core
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Preconditioners for the conjugate gradient algorithm using Gram-Schmidt and least squares methods
International Journal of Computer Mathematics
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This paper is devoted to the study of some preconditioned conjugate gradient algorithms on parallel computers. The considered preconditioners (presented in [J. Straubhaar, Preconditioners for the conjugate gradient algorithm using Gram-Schmidt and least squares methods, Int. J. Comput. Math. 84 (1) (2007) 89-108]) are based on incomplete Gram-Schmidt orthogonalization and least squares methods. The construction of the preconditioner and the resolution are treated separately. Numerical tests are performed and speed-up curves are presented in order to evaluate the performance of the algorithms.