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This book paints a fresco of the field of extrapolation and
rational approximation over the last several centuries to the
present through the works of their primary contributors. It can
serve as an introduction to the topics covered, including
extrapolation methods, Pade approximation, orthogonal polynomials,
continued fractions, Lanczos-type methods etc.; it also provides in
depth discussion of the many links between these subjects. A
highlight of this book is the presentation of the human side of the
fields discussed via personal testimonies from contemporary
researchers, their anecdotes, and their exclusive remembrances of
some of the "actors." This book shows how research in this domain
started and evolved. Biographies of other scholars encountered have
also been included. An important branch of mathematics is described
in its historical context, opening the way to new developments.
After a mathematical introduction, the book contains a precise
description of the mathematical landscape of these fields spanning
from the 19th century to the first part of the 20th. After an
analysis of the works produced after that period (in particular
those of Richardson, Aitken, Shanks, Wynn, and others), the most
recent developments and applications are reviewed.
This book paints a fresco of the field of extrapolation and
rational approximation over the last several centuries to the
present through the works of their primary contributors. It can
serve as an introduction to the topics covered, including
extrapolation methods, Pade approximation, orthogonal polynomials,
continued fractions, Lanczos-type methods etc.; it also provides in
depth discussion of the many links between these subjects. A
highlight of this book is the presentation of the human side of the
fields discussed via personal testimonies from contemporary
researchers, their anecdotes, and their exclusive remembrances of
some of the "actors." This book shows how research in this domain
started and evolved. Biographies of other scholars encountered have
also been included. An important branch of mathematics is described
in its historical context, opening the way to new developments.
After a mathematical introduction, the book contains a precise
description of the mathematical landscape of these fields spanning
from the 19th century to the first part of the 20th. After an
analysis of the works produced after that period (in particular
those of Richardson, Aitken, Shanks, Wynn, and others), the most
recent developments and applications are reviewed.
This expansive volume describes the history of numerical methods
proposed to solve linear algebra problems,, from antiquity to the
present day. The authors focus on methods for solving linear
systems of equations and eigenvalue problems and describe the
interplay between numerical methods and the computing tools
available at the time. The second part of the book consists of 78
biographies of the main important contributors to the field. A
Journey through the History of Numerical Linear Algebra will be of
special interest to applied mathematicians, especially researchers
in numerical linear algebra, and to applied mathematiciansas well
as to and historians of mathematics as well.
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