Mathematics and Computers in Simulation
SIAM Journal on Scientific and Statistical Computing
Iterative solution methods
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
Iterative methods for solving linear systems
Iterative methods for solving linear systems
Approximate sparsity patterns for the inverse of a matrix and preconditioning
IMACS'97 Proceedings on the on Iterative methods and preconditioners
Iterative solution of linear systems in the 20th century
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A Note on the Comparison of a Class of Preconditioned Iterative Methods
PCI '12 Proceedings of the 2012 16th Panhellenic Conference on Informatics
| Hi-index | 0.00 |
During the last decades, research efforts have been focused on the derivation of effective preconditioned iterative methods. The preconditioned iterative methods are mainly categorized into implicit preconditioned methods and explicit preconditioned methods. In this manuscript we review implicit preconditioned methods, based on incomplete and approximate factorization, and explicit preconditioned methods, based on sparse approximate inverses and explicit approximate inverses. Modified Moore-Penrose conditions are presented and theoretical estimates for the sensitivity of the explicit approximate inverse matrix of the explicit preconditioned method are derived. Finally, the performance of the preconditioned iterative methods is illustrated by solving characteristic 2D elliptic problem and numerical results are given indicating a qualitative agreement with the theoretical estimates.