How fast are nonsymmetric matrix iterations
SIAM Journal on Matrix Analysis and Applications
Calculation of pseudospectra by the Arnoldi iteration
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Parallel Preconditioning with Sparse Approximate Inverses
SIAM Journal on Scientific Computing
Iterative methods for solving linear systems
Iterative methods for solving linear systems
Experimental study of ILU preconditioners for indefinite matrices
Journal of Computational and Applied Mathematics
Iterative and Parallel Performance of High-Order Compact Systems
SIAM Journal on Scientific Computing
Approximate sparsity patterns for the inverse of a matrix and preconditioning
IMACS'97 Proceedings on the on Iterative methods and preconditioners
Preconditioned iterative methods and finite difference schemes for convection-diffusion
Applied Mathematics and Computation
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
Iterative methods preconditioned by incomplete factorizations and sparse approximate inverses are considered for solving linear systems arising from fourth-order finite difference schemes for convection-diffusion problems. Simple recurrences for implementing the ILU(0) factorization of the nine-point scheme are derived. Different sparsity patterns are considered for computing approximate inverses for the coefficient matrix and the quality of the preconditioner is studied in terms of plots of the field of values of the preconditioned matrices. In terms of algebraic properties of the preconditioned matrices, our experimental results show that incomplete factorizations give a preconditioner of better quality than approximate inverses. Comparison of the convergence rates of GMRES applied to the preconditioned linear systems is done with respect to the field of values, Ritz and harmonic Ritz values of the preconditioned matrices. Numerical results show that the GMRES residual norm decreases rapidly when the difference between the Ritz and harmonic Ritz values becomes small. We also describe the results of experiments when some well-known Krylov subspace methods are used to solve the linear system arising from the compact fourth-order discretizations.