\section{Introduction}
%
These are instructions for authors to prepare a manuscript for
proceedings published by the publishing house de Gruyter GmbH \& Co. KG, Berlin/New York.
Go to the subdirectory \verb1template1 and edit the file \verb1main.tex1.
This is the only file that has to be modified by authors.

\section{General information on the paper to be provided in the preamble of your document}
\label{authors}
%
The following commands have to be used in the preamble, i.e., they are to be placed before \verb1\begin{document}1.
\begin{itemize}
\item
Please provide \, author \, information \, by \, using \,  the \, commands \,
\verb1\authorx1, \, \verb1\addressx1, \,  \verb1\countryx1 and, if necessary,
\verb1\thanksx1. Here \texttt{x} can be \texttt{one}, \texttt{two},
\texttt{three}, or \texttt{four}.
By using the command \verb1\headlineauthor1,
you may generate a short version for author names in headlines.

\item
Please provide an abstract by the command \verb1\abstract1. 
It should be as brief as possible, and number of formulas used in their
should be kept to a minimum.

\item
Please provide keywords by the command \verb1\keywords1. The first word should be capitalized, others not except for namesxxxx. 
In addition, please provide an AMS 2000 classification by the command \verb2\classification2. Both keywords and classification numbers should be end up without full stop.

\item
If you want to include acknowledgments, please do this by using the command \verb1\acknowledgments1.
They in fact are printed at the end of your paper.%
\end{itemize}

\section{Your contribution}
In order to include your manuscript, you can make use of the \verb1\input1 command in
the file\ \verb1main.tex1, for example.
%
\subsection{Organizing your manuscript}
%
You may use sections, subsections and subsubsections.
In their titles, capitalize only the first word as well as names.
%
Use blank lines only if you wants to start a new paragraph.
Do not blank lines otherwise since the subsequent line is indented.

Footnotes should be as brief as possible, and their
number should be kept to a minimum.
Equations are numbered as (1.1), (1.2), \ldots, (2.1) etc., e.g.,
%
\begin{equation}
   1+1=2.
\end{equation}
%
In a definition, use italic fonts for the phrases to be defined.
%
\begin{definition}
   An $X$ satisfying $Y$ is called \emph{something}.
\end{definition}
%
\begin{remark}
In addition to the \verb2definition2 environment, several further
environments for structuring the exposition are provided and can be
accessed through commands like
\verb1\begin{algorithm}1\dots\verb1\end{algorithm}1. The following
environments are available:
%
   \begin{itemize}
      \item Algorithm, Assumption, Example, Remark and Proof, with the corresponding
text bodies typeset in roman, respectively.
      \item Corollary, Lemma, Proposition and Theorem,
      with the corresponding text bodies typeset in italic, 
respectively.
   \end{itemize}
\end{remark}
%
Please use always labels when referring to environments. For proofs of statements provided in environments, use the \verb1\begin{proof}1\dots\verb1\end{proof}1 environment.
%
%
\begin{theorem}
%%Each Thursday I am writing a paper.
Every day I am proving a theorem.
\end{theorem}
\begin{proof}
Is trivial. 
\end{proof}

\subsection{Figures}
%
Eps files may be included in the form%
\footnote{There are also options.}

\begin{verbatim}
  \begin{figure}[h]
    \centerline{\psfig{figure=figure1.eps,width=7cm} }
    \caption{\label{zzz}
      Text following the figure ...
    }
  \end{figure}
\end{verbatim}
%
Caption of figures and tables should be as brief as possible.

  \begin{figure}[h]
    \centerline{\psfig{figure=figure1.eps,width=7cm} }
    \caption{\label{zzz}
      Text following the figure \ldots
    }
  \end{figure}

\section{Bibliography}

For {\sc Bib}\TeX users, a style file \verb1wdg_proceedings.bst1 is provided. You
have to add your databases in the command \verb1\bibliography{}1.
%
Running
\begin{center}
   \verb1latex main1, \ \verb1bibtex main1, \ \verb1latex main1, \
   \verb1latex main1
\end{center}
%
will provide a file \verb1main.dvi1. (In case you are using references
within the bibliography, further executions of \verb1bibtex main1 and \verb1latex main1 may become necessary.) 
%%pdf files may be generated by the command \verb1pdflatex1. 
%%Please do not use \verb1dvips1 to generate postscript files, it do not work properly due to the used packages.

%%Links to web sites may be generated by the command \verb1\url{link}1 where \verb1link1 refers to the web adress. 
%%This in fact is a useful tool for the online version of your paper.



\nocite{Engl_Hanke_Neubauer[00]}
\nocite{Ashby_Manteuffel_Saylor[90]}
\nocite{Freund_Golub_Nachtigal[91]}
\nocite{Kammerer_Nashed[72]}
\nocite{Nemirovskii_Polyak[84.1]}
\nocite{Vainikko_Veretennikov[86]}
\nocite{Louis[87]}
\nocite{Eicke_Louis_Plato[90]}
\nocite{Fattorini[83]}
\nocite{Hanke[95.1]}
\nocite{Hanke[96.2]}
%

Here are the entries from the sample \verb1database.bib1 in the sample directory.

{
\footnotesize
\begin{verbatim}

@book{Engl_Hanke_Neubauer[00],
AUTHOR = { H.~W.~Engl and M.~Hanke and A.~Neubauer },
YEAR = {2000},
TITLE = { Regularization of Inverse Problems },
PUBLISHER = {Kluwer},
ADDRESS = {Dordrecht},
EDITION = {2nd}}

@article{Ashby_Manteuffel_Saylor[90],
AUTHOR = { S.~F.~Ashby and T.~A.~Manteuffel and P.~Saylor},
YEAR = {1990},
TITLE = { A taxomony for conjugate gradient methods },
JOURNAL = { SIAM J.~Numer.~Anal.},
VOLUME = { 27 },
NUMBER = { 6 },
PAGES = { 1542-1568 }}

@inproceedings{Freund_Golub_Nachtigal[91],
AUTHOR = { R.~W.~Freund and G.~H.~Golub and N.~M.~Nachtigal },
YEAR = {1991},
TITLE = { Iterative solution of linear systems },
BOOKTITLE = { Acta Numerica },
PUBLISHER = {Cambridge Univ.~Press},
ADDRESS = {Cambridge},
PAGES = { 1-44 }}

@article{Kammerer_Nashed[72],
AUTHOR = { W.~J.~Kammerer and M.~Z.~Nashed},
YEAR = {1972},
TITLE = { On the convergence of the
conjugate gradient method for singular linear operator equations },
JOURNAL = { SIAM J.~Numer.~Anal. },
VOLUME = {9},
NUMBER = {1},
PAGES = {165-181}}

@book{Vainikko_Veretennikov[86],
AUTHOR = { G.~M.~Vainikko and A.~Yu.~Veretennikov },
YEAR = {1986},
TITLE = { Iteration Procedures
in Ill-Posed Problems \textup{(in Russian)}},
PUBLISHER = {Nauka},
ADDRESS = {Moscow}}

@article{Eicke_Louis_Plato[90],
AUTHOR = { B.~Eicke and A.~K.~Louis and R.~Plato },
YEAR = {1990},
TITLE = { The instability of some
gradient methods for ill-posed problems},
JOURNAL = { Numer. Math. },
VOLUME = {58},
NUMBER = {1},
PAGES = {129-134}}

@inproceedings{Brakhage[87],
AUTHOR = { H. Brakhage },
YEAR = {1987},
TITLE = { On ill-posed problems and the method of conjugate gradients },
BOOKTITLE = { Inverse and Ill-Posed Problems, Proc. St. Wolfgang 1986 },
EDITOR = {H.~W.~Engl and C.~W.~Groetsch },
PUBLISHER = {Academic Press},
ADDRESS = {Boston},
PAGES = {165-175}}

@article{Nemirovskii_Polyak[84.1],
AUTHOR = {A.~S.~Nemirovski\u{\i} and B.~T.~Polyak },
YEAR = {1984},
TITLE = {Iterative methods for
solving linear ill-posed problems under precise information I },
JOURNAL = { Moscow Univ. Comput. Math. Cybern. },
VOLUME = {22},
NUMBER = {3},
PAGES = {1-11}}

@inproceedings{Louis[87],
AUTHOR = { A.~K. Louis },
YEAR = {1987},
TITLE = { Convergence of the conjugate gradient method
for compact operators },
BOOKTITLE = { Inverse and Ill-Posed Problems, Proc. St. Wolfgang 1986 },
EDITOR = {H.~W.~Engl and C.~W.~Groetsch},
PUBLISHER = {Academic Press},
ADDRESS = {Boston},
PAGES = {177-183}}

@book{Fattorini[83],
AUTHOR = {H.~O. Fattorini},
YEAR = {1983},
TITLE = { The Cauchy Problem },
PUBLISHER = {Addison-Wesley},
ADDRESS = {Reading}}

@book{Hanke[95.1],
AUTHOR = { M. Hanke },
YEAR = {1995},
TITLE = { Conjugate Gradient Type Methods for Ill-Posed Problems },
PUBLISHER = {Longman House},
ADDRESS = {Harlow}}

@article{Hanke[96.2],
AUTHOR = { M. Hanke },
YEAR = {1996},
TITLE = { Asymptotics of orthogonal polynomials
and the numerical solution of ill-posed problems },
JOURNAL = {Numer. Algor.},
VOLUME = {11},
NUMBER = {1-4},
PAGES = {203-214}}
\end{verbatim}} 
%
\normalsize
If you generate a bibliography without using {\sc Bib}\TeX,
please use the same style as presented in these author instructions.

