Rational Approximation and Interpolation PDF Download

Author: P.R. Graves-Morris
Publisher: Springer
ISBN: 3540391134
Category : Mathematics
Languages : en
Pages : 541

View

Book Description

Author: Joseph Leonard Walsh
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 426

View

Book Description

Author: P. R. Graves-Morris
Publisher:
ISBN: 9783662168851
Category :
Languages : en
Pages : 544

View

Book Description

Author: J. L. Walsh
Publisher: American Mathematical Soc.
ISBN: 0821810200
Category : Mathematics
Languages : en
Pages : 418

View

Book Description
The present work is restricted to the representation of functions in the complex domain, particularly analytic functions, by sequences of polynomials or of more general rational functions whose poles are preassigned, the sequences being defined either by interpolation or by extremal properties (i.e. best approximation). Taylor's series plays a central role in this entire study, for it has properties of both interpolation and best approximation, and serves as a guide throughout the whole treatise. Indeed, almost every result given on the representation of functions is concerned with a generalization either of Taylor's series or of some property of Taylor's series--the title ``Generalizations of Taylor's Series'' would be appropriate.

Author: Richard S. Varga
Publisher:
ISBN:
Category : Approximation theory
Languages : en
Pages : 148

View

Book Description

Author: Claude Brezinski
Publisher: Springer Nature
ISBN: 3030584186
Category : Mathematics
Languages : en
Pages : 410

View

Book Description
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.

Author:
Publisher:
ISBN:
Category : Approximation theory
Languages : en
Pages : 498

View

Book Description

Author: Johan Karlsson
Publisher:
ISBN:
Category : Approximation theory
Languages : en
Pages : 34

View

Book Description

Author: Peter Russell Graves-Morris
Publisher:
ISBN:
Category :
Languages : en
Pages : 528

View

Book Description

Author: Joseph Ball
Publisher: Birkhäuser
ISBN: 3034877099
Category : Science
Languages : en
Pages : 616

View

Book Description
This book aims to present the theory of interpolation for rational matrix functions as a recently matured independent mathematical subject with its own problems, methods and applications. The authors decided to start working on this book during the regional CBMS conference in Lincoln, Nebraska organized by F. Gilfeather and D. Larson. The principal lecturer, J. William Helton, presented ten lectures on operator and systems theory and the interplay between them. The conference was very stimulating and helped us to decide that the time was ripe for a book on interpolation for matrix valued functions (both rational and non-rational). When the work started and the first partial draft of the book was ready it became clear that the topic is vast and that the rational case by itself with its applications is already enough material for an interesting book. In the process of writing the book, methods for the rational case were developed and refined. As a result we are now able to present the rational case as an independent theory. After two years a major part of the first draft was prepared. Then a long period of revising the original draft and introducing recently acquired results and methods followed. There followed a period of polishing and of 25 chapters and the appendix commuting at various times somewhere between Williamsburg, Blacksburg, Tel Aviv, College Park and Amsterdam (sometimes with one or two of the authors).