GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
CGS, a fast Lanczos-type solver for nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
Algebraic multilevel preconditioning methods, II
SIAM Journal on Numerical Analysis
Factorized sparse approximate inverse preconditionings I: theory
SIAM Journal on Matrix Analysis and Applications
Local bisection refinement for N-simplicial grids generated by reflection
SIAM Journal on Scientific Computing
A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
Downwind numbering: robust multigrid for convection—diffusion problems
Applied Numerical Mathematics - Special issue on multilevel methods
Parallel Preconditioning with Sparse Approximate Inverses
SIAM Journal on Scientific Computing
A Sparse Approximate Inverse Preconditioner for Nonsymmetric Linear Systems
SIAM Journal on Scientific Computing
Toward an Effective Sparse Approximate Inverse Preconditioner
SIAM Journal on Matrix Analysis and Applications
Finite element solution of boundary value problems: theory and computation
Finite element solution of boundary value problems: theory and computation
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Sparse Approximate Inverses and Target Matrices
SIAM Journal on Scientific Computing
Partial Differential Equations: Modeling, Analysis, Computation (Siam Monographs on Mathematical Modeling and Computation) (Saim Models on Mathematical Modeling and Computation)
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For a one-dimensional diffusion problem on an refinedcomputational grid we present preconditioners based on the standardapproximate inverse technique. Next, we determine its spectralcondition number κ2 and perform numericalcalculations which corroborate the theoretical results. Then weperform numerical calculations which show that the standardapproximate inverse preconditioners and our modified versionsbehave in a similar manner. To finish with we show that acombination of the standard approximate inverse with an additionalincomplete factorisation leads to an almost optimal orderpreconditioner in 1 3 dimensions on refined grids, with and withoutdominant convection.