\documentstyle{article}
\newcommand{\J}{${\cal J}$}
\title{ANALYTICAL AND NUMERICAL STUDIES OF THE CONVERGENCE BEHAVIOR
OF THE \J\ TRANSFORMATION\footnote{Regensburg TC-NA-94-4 (Oct 17, 1994), J.
Comput. Appl. Math., in press.}}
\author{Herbert H. H. Homeier\\
  Institut f\"ur   Physikalische und Theoretische Chemie\\
  Universit\"a„t Regensburg\\
  D-93040 Regensburg\\
  Germany\\
  na.hhomeier@na-net.ornl.gov}
\date{}  
\begin{document}
\maketitle
\section*{ABSTRACT}
A new nonlinear sequence transformation, the iterative \J\
transformation, was proposed recently [H.\ H.\ H.\ Homeier, Some
applications of nonlinear convergence accelerators, {\it Int.\ J.\ Quantum
Chem.} {\bf 45}, 545 - 562 (1993)]. For this transformation, a
derivation based on the method of hierarchical consistency, alternative
recursive representations, general properties, an explicit expression
for the kernel, model sequences, and its relation to other sequence
transformations have been given [H.\ H.\ H.\ Homeier, A
hierarchically consistent, iterative sequence transformation, {\it Numer.\
Algo.} {\bf 8} (1994) 47-81]. The \J\ transformation is of similar generality as
the well-known E algorithm [C.\ Brezinski, A general extrapolation
algorithm, {\it Numer.\ Math.} {\bf 35}, 175 - 180 (1980). T.\ H{\aa}vie,
Generalized Neville type extrapolation schemes, {\it BIT} {\bf 19}, 204
- 213 (1979)]. In the present contribution, some results on convergence
acceleration properties of the \J\ transformation are proved. Numerical
test results are presented which show that the \J\
transformation is a very powerful computational tool for
convergence acceleration, extrapolation, and summation of
divergent series.

\vskip 1 cm\noindent
{\bf Keywords:}
Convergence acceleration --- Extrapolation --- Summation of
divergent series --- Hierarchical consistency --- Iterative
sequence transformations ---
Levin-type transformations --- $E$ algorithm --- Linear convergence ---
Logarithmic convergence --- Stieltjes series ---

\vskip 0.5 cm\noindent
{\bf Subject Classifications:}
AMS(MOS): 65B05 65B10


\end{document}