This free ebook volume is a self-contained, exhaustive exposition of the extrapolation
methods theory, and of the various algorithms and procedures for accelerating
the convergence of scalar and vector sequences. Many subroutines (written in
FORTRAN 77) with instructions for their use are provided on a floppy disk in
order to demonstrate to those working with sequences the advantages of the use
of extrapolation methods. Many numerical examples showing the effectiveness of
the procedures and a consequent chapter on applications are also provided –
including some never before published results and applications. Although
intended for researchers in the field, and for those using extrapolation methods
for solving particular problems, this volume also provides a valuable resource
for graduate courses on the subject.

The aim of this free ebook is twofold. First it is a self-contained and, as
much as possible, exhaustive exposition of the theory of extrapolation
methods and of the various algorithms and procedures for accelerating
the convergence of scalar and vector sequences. Our second aim is to
convince people working with sequences to use extrapolation methods
and to help them in this respect. This is the reason why we provide many
subroutines (written in FORTRAN 77) with their directions for use. We
also include many numerical examples showing the effectiveness of the
procedures and a quite consequent chapter on applications. In order to
reduce the size of the free book the proofs of the theoretical results have been
omitted and replaced by references to the existing literature. However,
on the other hand, some results and applications are given here for the
first time. We have also included suggestions for further research.

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