The talk describes the recent development in parallel preconditioning for solving sparse linear systems. The introduced iterative construction of Incomplete LU factorizations allows the efficient parallel construction of triangular preconditioners. Hence, the remaining bottleneck is the parallel triangular sparse solver.
For sparse triangular matrices we propose the use of incomplete sparse approximate inverses that on the one side can be seen as a generalization of the block Jacobi method and on the other side as a simplification of sparse approximate inverses.
By numerical examples we will show that especially for sparse triangular matrices these preconditioners and the related stationary solvers are very well suited.