Numerical solution of large sparse linear systems Ax=b by
KRYLOV SUBSPACE METHODS
Incomplete LU decomposition methods
Prescribe a bound and apply diagonal pivoting such that at any step k, and .
Strategy ensures that the
TEMPLATES THAT FORM ILUPACK
Template 1. Static reordering schemes.
Given system is reordered and scaled.
|Initial system||reordered and scaled system|
Template 2. Inverse-based ILU
with diagonal pivoting
After preordering and scaling the initial system, an inverse-based ILU with diagonal pivoting is applied.
controlled by diagonal pivoting
Template 3. Multilevel framework
For the reduced matrix that is left over from the second template, a recursive multilevel strategy is applied that repeatedly applies Templates 1 and 2.
Template 4. Iterative solver
After the incomplete LU decomposition is computed, the linear system is solved iteratively.