A stability analysis of incomplete LU factorizations
Mathematics of Computation
Modified incomplete factorization strategies
Proceedings of a conference on Preconditioned conjugate gradient methods
The convergence behaviour of preconditioned CG and CG-S in the presence of rounding errors
Proceedings of a conference on Preconditioned conjugate gradient methods
Nested grids ILU-decomposition (NGILU)
Proceedings of the 6th international congress on Computational and applied mathematics
ILUM: a multi-elimination ILU preconditioner for general sparse matrices
SIAM Journal on Scientific Computing
Matrix Renumbering ILU: An Effective Algebraic Multilevel ILU Preconditioner for Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
Solving Sparse Symmetric Sets of Linear Equations by Preconditioned Conjugate Gradients
ACM Transactions on Mathematical Software (TOMS)
A multigrid tutorial (2nd ed.)
A multigrid tutorial (2nd ed.)
Multigrid
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Adaptive Smoothed Aggregation ($\alpha$SA)
SIAM Journal on Scientific Computing
Preconditioning techniques for the solution of the Helmholtz equation by the finite element method
Mathematics and Computers in Simulation - Special issue: Wave phenomena in physics and engineering: New models, algorithms, and appications
SIAM Journal on Scientific Computing
A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems
SIAM Journal on Scientific Computing
A Parallel Multistage ILU Factorization Based on a Hierarchical Graph Decomposition
SIAM Journal on Scientific Computing
Spectral Analysis of the Discrete Helmholtz Operator Preconditioned with a Shifted Laplacian
SIAM Journal on Scientific Computing
Multilevel Adaptive Aggregation for Markov Chains, with Application to Web Ranking
SIAM Journal on Scientific Computing
Algebraic Multilevel Preconditioner for the Helmholtz Equation in Heterogeneous Media
SIAM Journal on Scientific Computing
Preconditioning Helmholtz linear systems
Applied Numerical Mathematics
SIAM Journal on Scientific Computing
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Standard (single-level) incomplete factorization preconditioners are known to successfully accelerate Krylov subspace iterations for many linear systems. The classical modified incomplete LU (MILU) factorization approach improves the acceleration given by (standard) ILU approaches, by modifying the nonunit diagonal in the factorization to match the action of the system matrix on a given vector, typically the constant vector. Here, we examine the role of similar modifications within the dual-threshold ILUT algorithm. We introduce column and row variants of the modified ILUT algorithm and discuss optimal ways of modifying the columns or rows of the computed factors to improve their accuracy and stability. Modifications are considered for both the diagonal and off-diagonal entries of the factors, based on one or many vectors, chosen a priori or through an Arnoldi iteration. Numerical results are presented to support our findings.