%% Authors:     David Young and Owe Axelsson
%% Title:       On generalized conjugate gradient type methods....
%% File initiated:  12/15/97
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\title{ On generalized conjugate gradient type methods for the iterative
solution of nonsymmetric and/or indefinite systems of equations}
\author {Owe Axelsson\\
Faculty of Mathematics and Informatics\\
University of Nijmegen\\
The Netherlands\\
and\\
David Young\\
Center for Numerical Analysis\\
The University of Texas at Austin\\
Austin, TX 78712}

\begin{document}

\maketitle

\begin{abstract}

\nn The behaviour of iterative solution methods for linear systems of algebraic
equations, in general nonsymmetric and/or indefinite, are considered.
The methods analysed are generalized conjugate gradient methods of minimal
residual or orthogonal residual type using and extended set of vectors from a
Krylov set, defined by the preconditioned matrix $B$.\\
A general convergence result showing convergence for any matrix for which its
field of values does not contain the origin, is given. The rate of convergence
can be analysed using the spectrum of $B$ or using pseudo-eigenvalues, or more
generally field of values of $B$. For severely ill-conditioned and/or strongly
non-normal matrices convergence stagnation occurs but can be avoided using short
length versions of the methods and a new preconditioner after restart of the
method.\\
Other issues discussed are automatic truncation to a short length version, the
use of normal equations and efficient implementation of the methods.
\end{abstract}

\end{document}