On the relations between ILUs and factored approximate inverses.

Author(s) : Matthias Bollhöfer , Youcef Saad

The paper is published : SIAM J. Matrix Anal. Appl., 24(1):219--237, 2002.

MSC 2000

65F05 Direct methods for linear systems and matrix inversion

65F10 Iterative methods for linear systems

65F50 Sparse matrices

Abstract :
This paper discusses some relationships between Incomplete LU (ILU) factorization techniques and factored sparse approximate inverse (AINV) techniques. While ILU factorizations compute approximate LU factors of the coefficient matrix A, AINV techniques aim at building triangular matrices Z and W such that W^TAZ is approximately diagonal. The paper shows that certain forms of approximate inverse techniques amount to approximately inverting the triangular factors obtained from some variants of incomplete LU factorization of the original matrix. A few useful applications of these relationships will be overviewed.

Keywords : sparse matrices, Incomplete LU (ILU), variants of ILU,sparse approximate inverse, AINV