Block preconditioning and domain decomposition methods. II
Journal of Computational and Applied Mathematics - Special issue on iterative methods for the solution of linear systems
The interface probing technique in domain decomposition
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
A Priori Sparsity Patterns for Parallel Sparse Approximate Inverse Preconditioners
SIAM Journal on Scientific Computing
Factorized Sparse Approximate Inverses for Preconditioning
The Journal of Supercomputing
Sparse Approximate Inverses and Target Matrices
SIAM Journal on Scientific Computing
Iterative Methods for Toeplitz Systems (Numerical Mathematics and Scientific Computation)
Iterative Methods for Toeplitz Systems (Numerical Mathematics and Scientific Computation)
An efficient parallel implementation of the MSPAI preconditioner
Parallel Computing
Smoothing and regularization with modified sparse approximate inverses
Journal on Image and Video Processing - Special issue on iterative signal processing in communications
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In this paper we introduce a new method for defining preconditioners for the iterative solution of a system of linear equations. By generalizing the class of modified preconditioners (e.g. MILU), the interface probing, and the class of preconditioners related to the Frobenius norm minimization (e.g. FSAI, SPAI) we develop a toolbox for computing preconditioners that are improved relative to a given small probing subspace. Furthermore, by this MSPAI (modified SPAI) probing approach we can improve any given preconditioner with respect to this probing subspace. All the computations are embarrassingly parallel. Additionally, for symmetric linear system we introduce new techniques for symmetrizing preconditioners. Many numerical examples, e.g. from PDE applications such as domain decomposition and Stokes problem, show that these new preconditioners often lead to faster convergence and smaller condition numbers.