The incomplete block decomposition based on Pade approximants

In this paper, we present a preconditioner for large systems of linear equations based on the incomplete block decomposition for block tridiagonal matrices. This method generalizes methods developed previously. Practical realization of this method for the model problem is similar to the realization of the method of complete matrix factorization. For more general matrices it is similar to the realization of the method constructed by one of the authors. However, in both cases the regarded method is more effective then the last ones.