  In this paper we introduce an algebraic recursive multilevel incomplete
factorization preconditioner, based on a distributed Schur complement
formulation, for solving general linear systems. The novelty of the proposed
method is to combine factorization techniques of both implicit and explicit
type, recursive combinatorial algorithms, multilevel mechanisms and overlapping
strategies to maximize sparsity in the inverse factors and consequently reduce
the factorization costs. Numerical experiments demonstrate the good potential
of the proposed solver to precondition effectively general linear systems, also
against other state-of-the-art iterative solvers of both implicit and explicit
form.
