On incomplete block factorization methods for matrices with complicated structure

Two classes of $SSOR$-type incomplete block factorization methods are proposed for preconditioning of linear algebraic systems of equations with block banded matrices of complex structure. Correctness conditions are derived for these methods in application to $M$-matrices and their efficiency is demonstrated by numerical experiments with linear algebraic systems obtained by discretization of the three-dimensional Poisson equation using quadratic and cubic serendipity finite elements.