Crout Versions of ILU for General Sparse Matrices

This paper presents an e cient implementation of incomplete LU (ILU) factorizations that are derived from the Crout version of Gaussian elimination (GE). At step k of the elimination, the k-th row of U and the k-th column of L are computed using previously computed rows of U and columns of L. The data structure and implementation borrow from already known techniques used in developing both sparse direct solution codes and incomplete Cholesky factorizations. It is shown that this version of ILU has many practical advantages. In particular, its data structure allows e cient implementation of more rigorous and e ective dropping strategies. Numerical tests show that the method is far more e cient than standard threshold-based ILU factorizations computed row-wise or column-wise.