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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, Padé 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.
List of contents
1. General Overview.- 2. Mathematical Background.- 3. The Mathematical Landscape up to the Mid-Twentieth Century.- 4. The Life of Peter Wynn.- 5. The Works of Peter Wynn. - 6. Commentaries and Further Developments.- 7. Testimonies.- 8. Vitae.- As a conclusion.- Acknowledgements.- Bibliography.- Index.
About the author
Claude Brezinski is professor emeritus of mathematics at the University of Lille (France), where he has been head of the Laboratory of Numerical Analysis and Optimization for 30 years. He was the advisor of 60 doctoral students. Prof. Brezinski is founder and Editor-in-Chief of the
Numerical Algorithms journal and author of over 240 papers and several books.
Michela Redivo-Zaglia is professor of numerical analysis at the University of Padua (Italy). She has been vice-director of the Department of Mathematics for three years. She is a member of the Editorial Board of several journals. She published software packages, 7 scientific and didactic books, and about 80 papers. She was the organizer of many international congresses, and an invited speaker at several more.
Report
"The reader goes deep into the research of the contributors, the monograph contains a quite precise description of the mathematical landscape of these subjects, formed by the mid-twentieth century." (Ralitza Kovacheva, Mathematical Reviews, May, 2022)
"This book ends with a conclusion and a bibliography of 816 items. Here an important branch of numerical analysis is impressively described in its historical context, opening a way to new developments." (Manfred Tasche, zbMATH 1477.65006, 2022)
