The convergence of certain incomplete block factorization splittings

This note fills a logical gap in the theory of incomplete block factorizations of generalized SSOR type. Namely, it shows that using the so-called factorized sparse approximate inverses it is possible to preserve the symmetry of an original Stieltjes or positive definite $H$-matrix $A$ in its incomplete block factorization $K$ and to ensure simultaneously the convergence of the related splitting $A=K-R$. Bibliography: 3 titles.