A parallel solver for large-scale Markov chains
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
New methods for adapting and for approximating inverses as preconditioners
Applied Numerical Mathematics - Developments and trends in iterative methods for large systems of equations—in memoriam Rüdiger Weiss
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
A Parallel Strongly Implicit Algorithm for Solving of Diffusion Equations
ParNum '99 Proceedings of the 4th International ACPC Conference Including Special Tracks on Parallel Numerics and Parallel Computing in Image Processing, Video Processing, and Multimedia: Parallel Computation
Ground Water Flow Modelling in PVM
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Inexact Newton Methods and Mixed Nonlinear Complementary Problems
NAA '00 Revised Papers from the Second International Conference on Numerical Analysis and Its Applications
Applied Numerical Mathematics
Multilevel block ILU preconditioner for sparse nonsymmetric M-matrices
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An MPI Implementation of the SPAI Preconditioner on the T3E
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Some convergence estimates for algebraic multilevel preconditioners
Contemporary mathematics
Journal of Computational and Applied Mathematics
On computing of block ILU preconditioner for block tridiagonal systems
Journal of Computational and Applied Mathematics
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Applied Numerical Mathematics
International Journal of Computing Science and Mathematics
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Journal of Computational and Applied Mathematics
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Journal of Computational and Applied Mathematics
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Computers and Structures
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Journal of Computational and Applied Mathematics
A Block FSAI-ILU Parallel Preconditioner for Symmetric Positive Definite Linear Systems
SIAM Journal on Scientific Computing
Greville's method for preconditioning least squares problems
Advances in Computational Mathematics
Finite-element based sparse approximate inverses for block-factorized preconditioners
Advances in Computational Mathematics
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
Improved Balanced Incomplete Factorization
SIAM Journal on Matrix Analysis and Applications
Nonsymmetric Preconditioner Updates in Newton-Krylov Methods for Nonlinear Systems
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
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Mathematical and Computer Modelling: An International Journal
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SIAM Journal on Scientific Computing
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Computers & Mathematics with Applications
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Numerical Algorithms
A generalized Block FSAI preconditioner for nonsymmetric linear systems
Journal of Computational and Applied Mathematics
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This paper is concerned with a new approach to preconditioning for large, sparse linear systems. A procedure for computing an incomplete factorization of the inverse of a nonsymmetric matrix is developed, and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient--type methods. Some theoretical properties of the preconditioner are discussed, and numerical experiments on test matrices from the Harwell--Boeing collection and from Tim Davis's collection are presented. Our results indicate that the new preconditioner is cheaper to construct than other approximate inverse preconditioners. Furthermore, the new technique insures convergence rates of the preconditioned iteration which are comparable with those obtained with standard implicit preconditioners.