A new scheme of computing the approximate inverse preconditioner for the reduced linear systems

In this paper, we propose a new implementation of the Newton scheme of an approximate preconditioner for the reduced linear system. In the original Newton scheme, the trouble is that the computation cost of the matrix–matrix product is always so expensive. On the other hand, the proposed implementation computes the preconditioner implicitly and reduces the cost of constructing the preconditioner by using the matrix–vector product form. We also show that the proposed implementation is less expensive than computing the preconditioner in explicit form.