Pade Approximants (Encyclopedia of Mathematics and its Applications)

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9780521135092: Pade Approximants (Encyclopedia of Mathematics and its Applications)
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This second edition is a comprehensive treatment of all straightforward aspects of Padé approximation, and the authors develop some themes to the level of current research. They extensively cover applications to statistical mechanics and critical phenomena, and there are newly extended sections devoted to circuit design, matrix Padé approximation, computational methods, and integral and algebraic approximants. The new edition also contains a chapter on multiseries approximants. The book contains an extensive bibliography of recent monographs on other specialized material. This succinct and straightforward treatment will appeal to scientists, engineers, and mathematicians alike.

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The first edition of this book was reviewed in 1982 as "the most extensive treatment of Pade approximants actually available." This second edition has been thoroughly updated, with a substantial new chapter on multiseries approximants. Applications to statistical mechanics and critical phenomena are extensively covered, and there are newly extended sections devoted to circuit design, matrix Pade approximation, and computational methods. This succinct and straightforward treatment will appeal to scientists, engineers, and mathematicians alike.

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The Pade approximant of a given power series is a rational function of numerator degree L and denominator degree M whose power series agrees with the given one up to degree L + M inclusively. A collection of Pade approximants formed by using a suitable set of values of L and M often provides a means of obtaining information about the function outside its circle of convergence, and of more rapidly evaluating the function within its circle of convergence. Applications of these ideas in physics, chemistry, electrical engineering, and other areas have led to a large number of generalizations of Pade approximants that are tailor-made for specific applications. Applications to statistical mechanics and critical phenomena are extensively covered, and there are newly extended sections devoted to circuit design, matrix Pade approximation, computational methods, and integral and algebraic approximants. The book is written with a smooth progression from elementary ideas to some of the frontiers of research in approximation theory. Its main purpose is to make the various techniques described accessible to scientists, engineers, and other researchers who may wish to use them, while also presenting the rigorous mathematical theory.

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9780521450072: Padé Approximants (Encyclopedia of Mathematics and its Applications)

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ISBN 10:  0521450071 ISBN 13:  9780521450072
Publisher: Cambridge University Press, 1996
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