Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Domain decomposition preconditioning for parallel PDE software
Engineering computational technology
Factorized Sparse Approximate Inverses for Preconditioning
The Journal of Supercomputing
Clustering method for fast deformation with constraints
Proceedings of the 2005 ACM symposium on Solid and physical modeling
International Journal of High Performance Computing Applications
Journal of Computational and Applied Mathematics
An efficient large deformation method using domain decomposition
Computers and Graphics
On computing of block ILU preconditioner for block tridiagonal systems
Journal of Computational and Applied Mathematics
Numerical performance of incomplete factorizations for 3D transient convection-diffusion problems
Advances in Engineering Software
On solving complex-symmetric eigenvalue problems arising in the design of axisymmetric VCSEL devices
Applied Numerical Mathematics
New breakdown-free variant of AINV method for nonsymmetric positive definite matrices
Journal of Computational and Applied Mathematics
Mixed Constraint Preconditioners for the iterative solution of FE coupled consolidation equations
Journal of Computational Physics
Applied Numerical Mathematics
Breakdown-free version of ILU factorization for nonsymmetric positive definite matrices
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Updating preconditioners for nonlinear deblurring and denoising image restoration
Applied Numerical Mathematics
Updating incomplete factorization preconditioners for shifted linear systems arising in a wind model
Journal of Computational and Applied Mathematics
Improved Balanced Incomplete Factorization
SIAM Journal on Matrix Analysis and Applications
Robust Approximate Cholesky Factorization of Rank-Structured Symmetric Positive Definite Matrices
SIAM Journal on Matrix Analysis and Applications
Efficient Preconditioner Updates for Shifted Linear Systems
SIAM Journal on Scientific Computing
Advances in Engineering Software
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
Adaptive Pattern Research for Block FSAI Preconditioning
SIAM Journal on Scientific Computing
Banded target matrices and recursive FSAI for parallel preconditioning
Numerical Algorithms
On numerical modeling performance of generalized preconditioned methods
Proceedings of the 6th Balkan Conference in Informatics
A generalization of the optimal diagonal approximate inverse preconditioner
Computers & Mathematics with Applications
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We present a variant of the AINV factorized sparse approximate inverse algorithm which is applicable to any symmetric positive definite matrix. The new preconditioner is breakdown-free and, when used in conjunction with the conjugate gradient method, results in a reliable solver for highly ill-conditioned linear systems. We also investigate an alternative approach to a stable approximate inverse algorithm, based on the idea of diagonally compensated reduction of matrix entries. The results of numerical tests on challenging linear systems arising from finite element modeling of elasticity and diffusion problems are presented.