\documentstyle[12pt]{article} \pagestyle{plain} \renewcommand{\Large}{\large}\renewcommand{\LARGE}{\large\bf} \author{ Maxim Larin \\ {\small Institute of Numerical Mathematics and Mathematical Geophysics SD RAS,} \\ {\small Novosibirsk, Russia. E-mail:~max@lapasrv.sscc.ru }} \title{ An Optimal Incomplete Factorization \\ Method for Stieltjes matrices \thanks{This work is a part of the Joint Research Project founded by INTAS and the Russian Foundation for the Basic Research within the framework of Cooperation Agreement INTAS--RFBR 95--0098, and was also partially supported by the Russian Foundation for the Basic Research grant 96-01-01770.}} .}} \date{} \begin{document} \maketitle Recently an algebraic multilevel incomplete factorization (AMLIF) method for solving large linear systems with Stieltjes matrices has been proposed. This method is a combination of two well-known techniques: algebraic multilevel (AMLI) and relaxed incomplete factorization (RIC). However, the efficiency of AMLIF method strongly depends on the choice of the relaxation parameter $\Theta$, an optimal value of which depends from the problem to be solved. Recently, dynamically relaxed incomplete factorization (DRIC) method that dynamically computes the corresponding problem-dependence value of $\Theta$, which are guarantee the good convergence properties, has been introduced. In the present paper we propose to use the block version of the DRIC method to construct an approximation of the Schur's complement as a new matrix on the lower level in the AMLI framework. \begin{thebibliography}{99} \bibitem{1} M.~Larin, {\em Algebraic multilevel incomplete factorization method for Stieltjes matrices}, to appear in Journal of Computational Mathematics and Mathematical Physics, 38(5), 1998 (in Russian). \bibitem{2} Y.~Notay, {\em DRIC: A Dinamic Version of the RIC Methods}, J. Num. Lin. Alg. with Appl., 1 (1994), pp.~511--532. \end{thebibliography} \end{document} 