Introduction to algorithms
Handbook of algorithms and data structures: in Pascal and C (2nd ed.)
Handbook of algorithms and data structures: in Pascal and C (2nd ed.)
Preconditioning for boundary integral equations
SIAM Journal on Matrix Analysis and Applications
Factorized sparse approximate inverse preconditionings I: theory
SIAM Journal on Matrix Analysis and Applications
Parallel Preconditioning with Sparse Approximate Inverses
SIAM Journal on Scientific Computing
Approximate Inverse Preconditioners via Sparse-Sparse Iterations
SIAM Journal on Scientific Computing
On a Class of Preconditioning Methods for Dense Linear Systems from Boundary Elements
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
Sparse Approximate Inverse Smoother for Multigrid
SIAM Journal on Matrix Analysis and Applications
Multilevel algorithms for multi-constraint graph partitioning
SC '98 Proceedings of the 1998 ACM/IEEE conference on Supercomputing
MPI-The Complete Reference, Volume 1: The MPI Core
MPI-The Complete Reference, Volume 1: The MPI Core
Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
Parallel Implementation of a Sparse Approximate Inverse Preconditioner
IRREGULAR '96 Proceedings of the Third International Workshop on Parallel Algorithms for Irregularly Structured Problems
EuroPVM '96 Proceedings of the Third European PVM Conference on Parallel Virtual Machine
An MPI Implementation of the SPAI Preconditioner on the T3E
International Journal of High Performance Computing Applications
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
hypre: A Library of High Performance Preconditioners
ICCS '02 Proceedings of the International Conference on Computational Science-Part III
Journal of Computational Physics
Conceptual interfaces in hypre
Future Generation Computer Systems
Conceptual interfaces in hypre
Future Generation Computer Systems
An efficient parallel implementation of the MSPAI preconditioner
Parallel Computing
Adaptive Techniques for Improving the Performance of Incomplete Factorization Preconditioning
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Parallel acceleration of krylov solvers by factorized approximate inverse preconditioners
VECPAR'04 Proceedings of the 6th international conference on High Performance Computing for Computational Science
Parallel hybrid sparse solvers through flexible incomplete cholesky preconditioning
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
An Empirical Analysis of the Performance of Preconditioners for SPD Systems
ACM Transactions on Mathematical Software (TOMS)
Parallel multigrid algorithms based on generic approximate sparse inverses: an SMP approach
The Journal of Supercomputing
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This paper describes and tests a parallel message-passing code for constructing sparse approximate inverse preconditioners using Frobenius norm minimization. The sparsity patterns of the preconditioners are chosen as patterns of powers of sparsified matrices. Sparsification is necessary when powers of a matrix have a large number of nonzeros, making the approximate inverse computation expensive. For our test problems, the minimum solution time is achieved with approximate inverses with less than twice the number of nonzeros of the original matrix. Additional accuracy is not compensated by the increased cost per iteration. The results lead to further understanding of how to use these methods and how well these methods work in practice. In addition, this paper describes programming techniques required for high performance, including one-sided communication, local coordinate numbering, and load repartitioning.