Factorized sparse approximate inverse preconditionings III. Iterative construction of preconditioners.

This paper presents new results of the theoretical study of factorized sparse approximate inverse (FSAI)preconditioners. In particular, the effect of the a posteriori Jacobi scaling and the possibility of constructing such preconditioners iteratively are analyzed. A simple stopping criterion for the termination of local iterations for constructing approximate FSAI preconditioners using the PCG method is proposed. The results of numirical experimernts with 3D finite-element problems from linear elasticity are presented.