In this talk we will present an ILU with pivoting that monitors the growth of
the inverse triangular factors of the decomposition. This information is used
to control dropping of ``small'' entries. The goal of this kind of dropping
is to construct more robust preconditioners.
We will discuss how the information
of the inverse
triangular factors is coupled with the dropping and the pivoting process.
Two versions
of this ILU based on adapting existing algorithms will be
presented.
One version is based on MA50,
a sparse direct Gaussian elimination method
from the Harwell Subroutine Library.
Another version
is constructed from ILUTP, an incomplete LU decomposition from SPARSKIT.
The improvements are illustrated for several numerical examples.
Keywords: sparse matrices, ILU, sparse
approximate inverse, condition estimation, pivoting.
AMS subject classification: 65F05, 65F10, 65F50.