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In this paper we consider several techniques for construction of general-purpose ILU preconditionings. We also provide some new theoretical results supporting the proposed preconditioning strategy. For the preprocession stage we consider row/column norm-equalizing two-side scaling, as well as diagonal dominance improvement by unsymmetric permutations. Within the incomplete LU-factorization, we use a variant of the inverse norm-reducing Complete Diagonal Pivoting. Numerical results are given for 67 test problems chosen from publicly available matrix sets.

Scaling, reordering, and diagonal pivoting in ILU preconditionings