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Author: Joseph Leonard Walsh
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 426
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Book Description
Author: Joseph Leonard Walsh
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 426
Get Book Here
Book Description
Author: P.R. Graves-Morris
Publisher: Springer
ISBN: 3540391134
Category : Mathematics
Languages : en
Pages : 541
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Book Description
Author: Claude Brezinski
Publisher: Springer Nature
ISBN: 3030584186
Category : Mathematics
Languages : en
Pages : 410
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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: J. L. Walsh
Publisher: American Mathematical Soc.
ISBN: 0821810200
Category : Mathematics
Languages : en
Pages : 418
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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: P. P. Petrushev
Publisher: Cambridge University Press
ISBN: 9780521177405
Category : Mathematics
Languages : en
Pages : 388
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Book Description
This 1987 book examines the approximation of real functions by real rational functions. These are a more convenient tool than polynomials, and interest in them was growing, especially after D. Newman's work in the mid-sixties. The authors present the basic achievements of the subject and also discuss some topics from complex rational approximation.
Author: Lloyd N. Trefethen
Publisher: SIAM
ISBN: 1611975948
Category : Mathematics
Languages : en
Pages : 377
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Book Description
This is a textbook on classical polynomial and rational approximation theory for the twenty-first century. Aimed at advanced undergraduates and graduate students across all of applied mathematics, it uses MATLAB to teach the fields most important ideas and results. Approximation Theory and Approximation Practice, Extended Edition differs fundamentally from other works on approximation theory in a number of ways: its emphasis is on topics close to numerical algorithms; concepts are illustrated with Chebfun; and each chapter is a PUBLISHable MATLAB M-file, available online. The book centers on theorems and methods for analytic functions, which appear so often in applications, rather than on functions at the edge of discontinuity with their seductive theoretical challenges. Original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. In addition, each chapter has a collection of exercises, which span a wide range from mathematical theory to Chebfun-based numerical experimentation. This textbook is appropriate for advanced undergraduate or graduate students who have an understanding of numerical analysis and complex analysis. It is also appropriate for seasoned mathematicians who use MATLAB.
Author: Joseph Ball
Publisher: Birkhäuser
ISBN: 3034877099
Category : Science
Languages : en
Pages : 616
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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).
Author: Detlef H. Mache
Publisher: Springer Science & Business Media
ISBN: 3764373563
Category : Mathematics
Languages : en
Pages : 300
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Book Description
This volume contains contributions from international experts in the fields of constructive approximation. This area has reached out to encompass the computational and approximation-theoretical aspects of various interesting fields in applied mathematics.
Author: Theodore J. Rivlin
Publisher: Courier Corporation
ISBN: 9780486640693
Category : Mathematics
Languages : en
Pages : 164
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Book Description
Mathematics of Computing -- Numerical Analysis.
Author: Dietrich Braess
Publisher: Springer Science & Business Media
ISBN: 3642616097
Category : Mathematics
Languages : en
Pages : 305
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Book Description
The first investigations of nonlinear approximation problems were made by P.L. Chebyshev in the last century, and the entire theory of uniform approxima tion is strongly connected with his name. By making use of his ideas, the theories of best uniform approximation by rational functions and by polynomials were developed over the years in an almost unified framework. The difference between linear and rational approximation and its implications first became apparent in the 1960's. At roughly the same time other approaches to nonlinear approximation were also developed. The use of new tools, such as nonlinear functional analysis and topological methods, showed that linearization is not sufficient for a complete treatment of nonlinear families. In particular, the application of global analysis and the consideration of flows on the family of approximating functions intro duced ideas which were previously unknown in approximation theory. These were and still are important in many branches of analysis. On the other hand, methods developed for nonlinear approximation prob lems can often be successfully applied to problems which belong to or arise from linear approximation. An important example is the solution of moment problems via rational approximation. Best quadrature formulae or the search for best linear spaces often leads to the consideration of spline functions with free nodes. The most famous problem of this kind, namely best interpolation by poly nomials, is treated in the appendix of this book.
