Iterative ILU Preconditioners for Linear Systems and Eigenproblems

Abstract

Iterative ILU factorizations are constructed, analyzed and applied as preconditioners to solve both linear systems and eigenproblems. The computational kernels of these novel Iterative ILU factorizations are sparse matrix-matrix multiplications, which are easy and efficient to implement on both serial and parallel computer architectures and can take full advantage of existing matrix-matrix multiplication codes. We also introduce level-based and threshold-based algorithms in order to enhance the accuracy of the proposed Iterative ILU factorizations. The results of several numerical experiments illustrate the efficiency of the proposed preconditioners to solve both linear systems and eigenvalue problems.