\documentstyle{article}
\newcommand{\J}{${\cal{J}}$}
\begin{document}
%
\title{
Determinantal representations for the \\
\J\ transformation\footnote{Regensburg preprint TC-NA-94-5 (Dec 9, 1994), Numer. Math., in press.}
}
\author{Herbert H. H. Homeier\thanks{E-mail: na.hhomeier@na-net.ornl.gov}\\\
  Institut f\"ur Physikalische und Theoretische Chemie,\\
  Universit\"at Regensburg,
\\
  D-93040 Regensburg,
  Germany
}
\date{Received May 24, 1994}
\maketitle
%
\begin{abstract}
The iterative \J\ transformation [Homeier, H.\ H.\ H. (1993): {
Some applications of nonlinear convergence accelerators}. Int.\
J.\ Quantum Chem.\ {\bf 45}, 545--562] is of similar generality
as the well-known E algorithm [Brezinski, C. (1980): {A general
ex\-tra\-po\-la\-tion algorithm}. Numer.\ Math.\ {\bf 35}, 175--180.
H{\aa}vie, T. (1979): { Generalized Neville type ex\-tra\-po\-la\-tion
schemes}. BIT {\bf 19}, 204--213]. The properties of the \J\
transformation were studied recently in two companion papers
[Homeier, H.\ H.\ H. (1994a): A hierarchically consistent,
iterative sequence transformation. {Numer.\ Algo.} {\bf 8}, 47--81.
Homeier, H.\ H.\ H. (1994b): { Analytical and numerical studies
of the convergence behavior of the \J\ transformation}. J.\
Comput.\ Appl.\ Math., to appear].  In the present contribution,
explicit determinantal representations for this sequence
transformation are derived. The relation to the Brezinski-Walz
theory [Brezinski, C., Walz,  G. (1991): { Sequences of
transformations and triangular recursion schemes, with
applications in numerical analysis}. J.\ Comput.\ Appl.\ Math.\
{\bf 34}, 361--383] is discussed. Overholt's process [Overholt,
K.\ J. (1965): {Extended Aitken acceleration}. BIT {\bf 5},
122--132] is shown to be a special case of the \J\
transformation. Consequently, explicit determinantal representations
of Overholt's process are derived which do not depend
on lower order transforms. Also, families of sequences are given
for which Overholt's process is exact.
As a numerical example, the Euler series is
summed using the \J\ transformation. The results indicate that the \J\
transformation is a very powerful numerical tool.
\end{abstract}

\end{document}