In this paper we present several improvements of widely used parallel LU factorization
methods on sparse matrices. First we introduce the LU elimination forest and then we
characterize the L, U factors in terms of their corresponding LU elimination forest. This
characterization can be used as a compact storage scheme of the matrix as well as of the
task dependence graph. To improve the use of BLAS in the numerical factorization, we
perform a postorder traversal of the LU elimination forest, thus obtaining larger supernodes …

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