Incremental condition estimation
SIAM Journal on Matrix Analysis and Applications
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
Matrix computations (3rd ed.)
Estimating the Attainable Accuracy of Recursively Computed Residual Methods
SIAM Journal on Matrix Analysis and Applications
A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems
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
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Preconditioning Highly Indefinite and Nonsymmetric Matrices
SIAM Journal on Scientific Computing
Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
On the Relations between ILUs and Factored Approximate Inverses
SIAM Journal on Matrix Analysis and Applications
On Algorithms For Permuting Large Entries to the Diagonal of a Sparse Matrix
SIAM Journal on Matrix Analysis and Applications
A Robust and Efficient ILU that Incorporates the Growth of the Inverse Triangular Factors
SIAM Journal on Scientific Computing
Crout Versions of ILU for General Sparse Matrices
SIAM Journal on Scientific Computing
Preconditioning Sparse Nonsymmetric Linear Systems with the Sherman--Morrison Formula
SIAM Journal on Scientific Computing
Balanced Incomplete Factorization
SIAM Journal on Scientific Computing
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
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In this paper we improve the BIF algorithm which computes simultaneously the LU factors (direct factors) of a given matrix and their inverses (inverse factors). This algorithm was introduced in [R. Bru, J. Marín, J. Mas, and M. Tu˚ma, SIAM J. Sci. Comput., 30 (2008), pp. 2302-2318]. The improvements are based on a deeper understanding of the inverse Sherman-Morrison (ISM) decomposition, and they provide a new insight into the BIF decomposition. In particular, it is shown that a slight algorithmic reformulation of the basic algorithm implies that the direct and inverse factors numerically influence each other even without any dropping for incompleteness. Algorithmically, the nonsymmetric version of the improved BIF algorithm is formulated. Numerical experiments show very high robustness of the incomplete implementation of the algorithm used for preconditioning nonsymmetric linear systems.