New Evaluation Index of Orderings in Incomplete Factorization Preconditioning

| It is well known that ordering of unknowns greatly a ects convergence in Incomplete LU (ILU) factorization preconditioned iterative methods. The authors recently proposed a simple evaluation way for orderings in ILU preconditioning. The evaluation index, which has a simple relationship with a norm of a remainder matrix, is easily computed without additional memory requirement. The computational cost of the index is about the same as that of ILU factorization. The e ectiveness of the method is examined by numerical tests using coeÆcient matrix data obtained from Matrix Market.