GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Direct methods for sparse matrices
Direct methods for sparse matrices
Preconditioning techniques for nonsymmetric and indefinite linear systems
Journal of Computational and Applied Mathematics - Special issue on iterative methods for the solution of linear systems
Iterative solution methods
Overlapped multicolor MILU preconditioning
SIAM Journal on Scientific Computing
Matrix computations (3rd ed.)
CIMGS: An Incomplete Orthogonal Factorization Preconditioner
SIAM Journal on Scientific Computing
Sharp error bounds of some Krylov subspace methods for non-Hermitian linear systems
Applied Mathematics and Computation
Orderings for Factorized Sparse Approximate Inverse Preconditioners
SIAM Journal on Scientific Computing
Hermitian and Skew-Hermitian Splitting Methods for Non-Hermitian Positive Definite Linear Systems
SIAM Journal on Matrix Analysis and Applications
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A Robust Preconditioner with Low Memory Requirements for Large Sparse Least Squares Problems
SIAM Journal on Scientific Computing
Stopping criteria for iterations in finite element methods
Numerische Mathematik
Block Triangular and Skew-Hermitian Splitting Methods for Positive-Definite Linear Systems
SIAM Journal on Scientific Computing
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We design, analyse and test a class of incomplete orthogonal factorization preconditioners constructed from Givens rotations, incorporating some dropping strategies and updating tricks, for the solution of large sparse systems of linear equations. Comprehensive accounts about how the preconditioners are coded, what storage is required and how the computation is executed for a given accuracy are presented. A number of numerical experiments show that these preconditioners are competitive with standard incomplete triangular factorization preconditioners when they are applied to accelerate Krylov subspace iteration methods such as GMRES and BiCGSTAB.