A stability analysis of incomplete LU factorizations
Mathematics of Computation
Direct methods for sparse matrices
Direct methods for sparse matrices
Parallel Preconditioning with Sparse Approximate Inverses
SIAM Journal on Scientific Computing
Experimental study of ILU preconditioners for indefinite matrices
Journal of Computational and Applied Mathematics
Sparse Approximate-Inverse Preconditioners Using Norm-Minimization Techniques
SIAM Journal on Scientific Computing
A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
Approximate Inverse Preconditioners via Sparse-Sparse Iterations
SIAM Journal on Scientific Computing
The Design and Use of Algorithms for Permuting Large Entries to the Diagonal of Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
Algorithm 575: Permutations for a Zero-Free Diagonal [F1]
ACM Transactions on Mathematical Software (TOMS)
Preconditioning Highly Indefinite and Nonsymmetric Matrices
SIAM Journal on Scientific Computing
On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix
SIAM Journal on Matrix Analysis and Applications
A Multilevel Dual Reordering Strategy for Robust Incomplete LU Factorization of Indefinite Matrices
SIAM Journal on Matrix Analysis and Applications
MSP: A Class of Parallel Multistep Successive Sparse Approximate Inverse Preconditioning Strategies
SIAM Journal on Scientific Computing
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A new stabilization strategy for incomplete LU preconditioning of indefinite matrices
Applied Mathematics and Computation
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A two-phase preconditioning strategy based on a factored sparse approximate inverse is proposed for solving sparse indefinite matrices. In each phase, the strategy first makes the original matrix diagonally dominant to enhance the stability by a shifting method, and constructs an inverse approximation of the shifted matrix by utilizing a factored sparse approximate inverse preconditioner. The two inverse approximation matrices produced from each phase are then combined to be used as a preconditioner. Experimental results show that the presented strategy improves the accuracy and the stability of the preconditioner on solving indefinite sparse matrices. Furthermore, the strategy ensures that convergence rate of the preconditioned iterations of the two-phase preconditioning strategy is much better than that of the standard sparse approximate inverse ones for solving indefinite matrices.