GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
SIAM Journal on Scientific and Statistical Computing
Optimal and superoptimal circulant preconditioners
SIAM Journal on Matrix Analysis and Applications
Iterative solution methods
A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
Conjugate Gradient Methods for Toeplitz Systems
SIAM Review
Parallel Preconditioning with Sparse Approximate Inverses
SIAM Journal on Scientific Computing
Sparse Approximate-Inverse Preconditioners Using Norm-Minimization Techniques
SIAM Journal on Scientific Computing
Approximate Inverse Preconditioners via Sparse-Sparse Iterations
SIAM Journal on Scientific Computing
A comparative study of sparse approximate inverse preconditioners
IMACS'97 Proceedings on the on Iterative methods and preconditioners
Robust Approximate Inverse Preconditioning for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
MSP: A Class of Parallel Multistep Successive Sparse Approximate Inverse Preconditioning Strategies
SIAM Journal on Scientific Computing
Preconditioning techniques for large linear systems: a survey
Journal of Computational Physics
Preconditioners generated by minimizing norms
Computers & Mathematics with Applications
A family of modified regularizingcirculant preconditioners for two-levels Toeplitz systems
Computers & Mathematics with Applications
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
| Hi-index | 0.09 |
The classical optimal (in the Frobenius sense) diagonal preconditioner for large sparse linear systems Ax=b is generalized and improved. The new proposed approximate inverse preconditioner N is based on the minimization of the Frobenius norm of the residual matrix AM-I, where M runs over a certain linear subspace of nxn real matrices, defined by a prescribed sparsity pattern. The number of nonzero entries of the nxn preconditioning matrix N is less than or equal to 2n, and n of them are selected as the optimal positions in each of the n columns of matrix N. All theoretical results are justified in detail. In particular, the comparison between the proposed preconditioner N and the optimal diagonal one is theoretically analyzed. Finally, numerical experiments reported confirm the theory and illustrate that our generalization of the optimal diagonal preconditioner improves (in general) its efficiency, when they do not coincide.