ACM Transactions on Mathematical Software (TOMS)
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This paper presents a weighted dropping strategy for the matrix $L$ of the incomplete LU preconditioner with pivoting and dropping based on a dual threshold strategy (ILUTP). Preconditioners using this strategy often perform better than the standard ILUTP preconditioner for some difficult matrices. For matrices that are relatively easy to precondition, the results are similar. The implementation and setup times are somewhat longer than the ILUTP preconditioner employing the standard dropping strategy.