A sparse approximate inverse for triangular matrices based on Jacobi iteration

In this paper, we propose a sparse approximate inverse for triangular matrices (SAIT) based on Jacobi iteration. The main operation of the algorithm is matrix-matrix multiplication. We apply the SAIT to iterative methods with ILU preconditioners. Then the two triangular solvers in the ILU preconditioning procedure are replaced by two matrix-vector multiplications, which can be fine-grained parallelized. We test the new algorithm by solving some linear systems and eigenvalue problems.