Numerical solution of large sparse linear systems Ax=b by
Incomplete LU decomposition methods
Prescribe a bound and apply diagonal pivoting such that at any step k, and .
Strategy ensures that the
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.