Symmetric Permutations for I-Matrices to Avoid Small Pivots During In- complete Factorization

Incomplete LU-factorizations have been very successful as preconditioners for solving sparse linear systems iteratively. How-ever, for unsymmetric, indefinite systems small pivots (or even zero pivots) are often very detrimental to the quality of the preconditioner. A fairly recent strategy to deal with this problem has been to permute the rows of the matrix and to scale rows and columns to produce an I-matrix, a matrix having elements of modulus one on the diagonal and elements of at most modulus one elsewhere. These matrices are generally more suited for incomplete LU-factorization. I-matrices are preserved by symmetric permutation, i.e. by applying the same permutation to rows and columns of a matrix. We discuss different approaches for constructing such permutations which aim at improving the sparsity and diagonal dominance of an initial block. Copyright line will be provided by the publisher