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\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{}
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\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}