Padé Approximants (Encyclopedia of Mathematics and its Applications, Series Number 59) 2nd Edition by George A. Baker Jr (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review “The book is an absolute must for every starting researcher in the area of rational approximation theory….The book is written in smooth progression…” Annie A.M. Cuyt, Mathematical Reviews Book Description Thoroughly updated, with material on multiseries approximants, circuit design, matrix Padé approximation and computational methods. From the Back Cover 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. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐When I was in graduate school, there were a number of articles I came across by George Baker, and his work struck me as rather brilliant, while at the same time rather eccentric and missing the point and focusing far too much on the “trees” over the “forest”. It has been many years since I worked in series analysis after completing my PhD, but I got an idea for a paper related to some of the material covered in this book. I must say, on the plus side, that were it not for the excellent treatment of each topic my paper would simply have been impossible, as this was clearly the best recent reference I could find on series analysis. On the other hand, I still find, for all of his brilliance, that Baker fails to see the importance of some of the material he discusses in detailed and superficial ways. Overall, I highly recommend this book for research in series analysis.

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Padé Approximants (Encyclopedia of Mathematics and its Applications, Series Number 59) 2nd Edition PDF Free Download
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