Factorized sparse approximate inverse preconditionings I: theory
SIAM Journal on Matrix Analysis and Applications
Iterative solution methods
Parallel Preconditioning with Sparse Approximate Inverses
SIAM Journal on Scientific Computing
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
Approximate sparsity patterns for the inverse of a matrix and preconditioning
IMACS'97 Proceedings on the on Iterative methods and preconditioners
A Priori Sparsity Patterns for Parallel Sparse Approximate Inverse Preconditioners
SIAM Journal on Scientific Computing
Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
Reducing the bandwidth of sparse symmetric matrices
ACM '69 Proceedings of the 1969 24th national conference
Crout Versions of ILU for General Sparse Matrices
SIAM Journal on Scientific Computing
Sparse Approximate Inverses and Target Matrices
SIAM Journal on Scientific Computing
An Implicit Wavelet Sparse Approximate Inverse Preconditioner
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
A comparison of projective and direct solvers for finite elements in elastostatics
Advances in Engineering Software
A Block FSAI-ILU Parallel Preconditioner for Symmetric Positive Definite Linear Systems
SIAM Journal on Scientific Computing
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
Banded target matrices and recursive FSAI for parallel preconditioning
Numerical Algorithms
A generalized Block FSAI preconditioner for nonsymmetric linear systems
Journal of Computational and Applied Mathematics
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An adaptive algorithm is presented to generate automatically the nonzero pattern of the block factored sparse approximate inverse (BFSAI) preconditioner. It is demonstrated that in symmetric positive definite (SPD) problems BFSAI minimizes an upper bound to the Kaporin number of the preconditioned matrix. The mathematical structure of this bound suggests an efficient and easily parallelizable strategy for improving the given nonzero pattern of BFSAI, thus providing a novel adaptive BFSAI (ABF) preconditioner. Numerical experiments performed on large sized finite element problems show that ABF coupled with a block incomplete Cholesky (IC) outperforms BFSAI-IC even by a factor of 4, preserving the same preconditioner density and exhibiting an excellent parallelization degree.