Factorized sparse approximate inverse preconditionings I: theory
SIAM Journal on Matrix Analysis and Applications
Modification of the minimum-degree algorithm by multiple elimination
ACM Transactions on Mathematical Software (TOMS)
Parallel Preconditioning with Sparse Approximate Inverses
SIAM Journal on Scientific Computing
Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
Factorized Sparse Approximate Inverses for Preconditioning
The Journal of Supercomputing
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Factorized Sparse Approximate Inverses for Preconditioning
The Journal of Supercomputing
Frobenius norm minimization and probing for preconditioning
International Journal of Computer Mathematics - Fast Iterative and Preconditioning Methods for Linear and Non-Linear Systems
Sparse approximate inverse preconditioners for iterative solvers on GPUs
Proceedings of the 2012 Symposium on High Performance Computing
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
On scalability behaviour of Monte Carlo sparse approximate inverse for matrix computations
ScalA '13 Proceedings of the Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems
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In recent papers the use of sparse approximate inverses for the preconditioning of linear equations Ax=b is examined. The minimization of ||AM−I|| in the Frobenius norm generates good preconditioners without any a priori knowledge on the pattern of M. For symmetric positive definite A and a given a priori pattern there exist methods for computing factorized sparse approximate inverses L with LLT≈A−;1. Here, we want to modify these algorithms that they are able to capture automatically a promising pattern for L.We use these approximate inverses for solving linear equations with the cg-method. Furthermore we introduce and test modifications of this method for computing factorized sparse approximate inverses.