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\title{Regular Array for the Solution of Toeplitz System of Linear Equations by Monte Carlo Method}

\author{
V.~N.~Alexandrov and G.~Ok\v sa \thanks{Institute for Informatics, Slovak Academy of Sciences, Bratislava, and
Nuclear Power Plant Research Institute, Trnava, Slovak Republic. Funded by the Royal Society Postdoctoral
Fellowship Scheme.}\\
\small Department of Computer Sciences \\
\small University of Liverpool\\
\small Chadwick Building\\
\small Peach Street\\
\small Liverpool\\
\small L69 7ZF, UK }

\date{}

\begin{document}

\maketitle

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\abstract{
We propose a regular array for  solving  system of linear
 algebraic equations  with  an $n \times n$ Toeplitz
diagonally dominant matrix using a Monte Carlo method.
 The basic array computes a component of the vector
solution in $n+N+T$ steps (including input and output time) and
$3NT$ cells where $N$ is the  number of chains
and $T$ is the length of each chain in the stochastic process.
A whole solution vector is computed in time
$2n+N+T$ in the fully pipelined fashion and requires $3nNT$ cells.
A number of bounds on  $N$ and $T$ are
established which show that our design is faster than
existing designs for reasonably large values of $n$.

\noindent \vglue10pt {\em Keywords}\/: Toeplitz matrix, Monte Carlo method,
 System of Linear Algebraic
Equations, Regular Array

}eywords}\/: Toeplitz matrix, Monte Carlo method,
 System of Linear Algebraic
Equations, Regular Array

}eywords}oItsquateag
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\e{\ecument}

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