Iterative ILU Preconditioners for Linear Systems and Eigenproblems (Journal of Computational Mathematics, 2021)
Iterative ILU factorizations are constructed, analyzed and applied as preconditionersto solve both linear systems and eigenproblems. The computational kernels of these novelIterative ILU factorizations are sparse matrix-matrix multiplications, which are easy andefficient to implement on both serial and parallel computer architectures and can take fulladvantage of existing matrix-matrix multiplication codes. We also introduce level-basedand threshold-based algorithms in order to enhance the accuracy of the proposed IterativeILU factorizations. The results of several numerical experiments illustrate the efficiency ofthe proposed preconditioners to solve both linear systems and eigenvalue problems.
Keywords: Iterative ILU factorization; Matrix-matrix multiplication; Fill-in; Eigenvalue problem; Parallel preconditioner.