Several preconditioning enhancement strategies for improving inaccurate preconditioners produced by the incomplete LU factorizations of sparse matrices are presented. The strategies employ the elements that are dropped during the incomplete LU factorization and utilize them in different ways by separate algorithms.

The first strategy (error compensation) applies the dropped elements to the lower and upper parts of the LU factorization to computer a new error compensated LU factorization. Another strategy (inner-outer iteration), which is a variant of the incomplete LU factorization, embeds the dropped elements in its iteration process.

Experimental results show that the presented enhancement strategies improve the accuracy of the incomplete LU factorization when the initial factorizations found to be inaccurate. Furthermore, the convergence cost of the preconditioned Krylov subspace methods is reduced on solving the original sparse matrices with the proposed strategies.