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\title {Efficient Monte Carlo Algorithms for
Inverting Matrices Arising in Mixed Finite Element Approximation}

\author {T.T. Dimov $^{1}$}

\begin{document}
\maketitle

\footnotetext[1]{
Central Laboratory for Parallel
Processing, Department of
Parallel Algorithms, Bulgarian Academy of Sciences,
Acad.  G.  Bonchev St.,bl.  25 A, \,\, 1113 \,\, Sofia,
Bulgaria, e-mail: tdimov@iscbg.acad.bg, \,
Web site: http://www.acad.bg/BulRTD/math/dimov2.html}



\begin{abstract}

A new approach for inverting matrices arising after Raviart-Thomas
mixed finite element discretization of second-order elliptic
equations is studied. Two Monte Carlo algorithms are considered.

The first algorithm  is based on a special
techniques, which  uses different  relaxation parameters in the
iterative procedure and improves the inverse matrix approximation
column by column. The second algorithm derives a good error
balancing for these special matrices row by row.

All parameters determining the efficiency of the algorithms
are controled automatically by a posteriori criteria based
on some essential properties of the residual matrices.

Numerical computations for rectangular finite elements
are presented.
The  algorithms under consideration are well parallelized.
\end{abstract}

{\it Keywords:}
Monte Carlo algorithms, mixed finite element method, iterative methods,
Markov chain, inverse matrix  problem.

{\it  ASM subject classifications:}
65C05, 65U05, 65F10, 65Y20.

\end{document}