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\title{An Adaptive Restarting Procedure for Pseudo-Residual Methods}
\author{Takashi Nodera\\
Dept. of Math., Keio University,  \\
3-14-1 Hiyoshi Kohoku \\
Yokohama 223, Japan, \\
email: nodera@math.keio.ac.jp}
\date{}    
\maketitle
My talk is concerned with PRES(pseudo-residual) methods,
one of the iterative methods for solving large and sparse
nonsymmetric linear systems of equations. The main variants
of PRES methods are exact, restarted, truncated, and combined
methods. Unfortunately, in the exact methods, the storage 
requirements and the computational work increase with the 
iteration. The restarted and truncated methods also have the 
unstable convergence in some practical problems. It is generally 
to say that the combined methods can not breakdown, it is stable,
because these procedures based on the restarting process of the 
truncated methods. However, the combined methods that restart 
periodically represent bad convergence behavior in some case.
\vskip 2truemm

The possibility of the restarting technique may be exploited to
develop efficient algorithm and to enhance robustness. In this 
paper, we propose the new combined algorithm, which is called the 
adaptive combined PRES method, to monitor the convergence behavior 
of residual. This adaptive procedure is attractive because it only 
has the restarting process. 

\vskip 2truemm

At last, we present some numerical experiments to illustrate the 
above fact using the parallel computer AP1000.
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