J. Mas
A Balanced Incomplete Factorization preconditioner

Institut de Matemàtica Multidisciplinar
Universitat Politècnica de València
Camí de Vera
14
46022 València
Spain
jmasm@imm.upv.es
R. Bru
J. Marín
Tuma, M.

In [3] a factorized approximate inverse preconditioner (AISM) based on the Sherman-Morrison formula is presented. In this work the structure of the factors is analyzed and it is proved that the $L$ and $D$ factors of the $LDU$ factorization of a matrix are easily retrieved from one of them. Moreover columns of $L$ and $L^{-1}$ are computed in the same step which makes the application of dropping strategies proposed in [2] straightforward in the case of a symmetric positive definite coefficient matrix.

Numerical experiments on a set of symmetric positive definite matrices are done showing that this strategy, that we called Balanced Incomplete Factorization (BIF for short), is very robust for preconditioning very ill-conditioned problems using iterative methods. In addition BIF exhibits shorter setup times than RIF [1], a method of a similar and very high level of robustness.