The History Of Approximation Theory

Author : Karl-Georg Steffens
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 44,8 Mb
Release : 2007-07-28
Category : Mathematics
ISBN : 9780817644758

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The History of Approximation Theory by Karl-Georg Steffens Pdf

* Exciting exposition integrates history, philosophy, and mathematics * Combines a mathematical analysis of approximation theory with an engaging discussion of the differing philosophical underpinnings behind its development * Appendices containing biographical data on numerous eminent mathematicians, explanations of Russian nomenclature and academic degrees, and an excellent index round out the presentation

Author : Karl-Georg Steffens
Publisher : Unknown
Page : 128 pages
File Size : 46,8 Mb
Release : 2005
Category : Electronic
ISBN : 3764343532

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The History of Approximation Theory by Karl-Georg Steffens Pdf

Author : Lloyd N. Trefethen
Publisher : SIAM
Page : 375 pages
File Size : 50,6 Mb
Release : 2019-01-01
Category : Mathematics
ISBN : 9781611975949

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Approximation Theory and Approximation Practice, Extended Edition by Lloyd N. Trefethen Pdf

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 field’s 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 : M. J. D. Powell
Publisher : Cambridge University Press
Page : 356 pages
File Size : 51,9 Mb
Release : 1981-03-31
Category : Mathematics
ISBN : 0521295149

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Approximation Theory and Methods by M. J. D. Powell Pdf

Most functions that occur in mathematics cannot be used directly in computer calculations. Instead they are approximated by manageable functions such as polynomials and piecewise polynomials. The general theory of the subject and its application to polynomial approximation are classical, but piecewise polynomials have become far more useful during the last twenty years. Thus many important theoretical properties have been found recently and many new techniques for the automatic calculation of approximations to prescribed accuracy have been developed. This book gives a thorough and coherent introduction to the theory that is the basis of current approximation methods. Professor Powell describes and analyses the main techniques of calculation supplying sufficient motivation throughout the book to make it accessible to scientists and engineers who require approximation methods for practical needs. Because the book is based on a course of lectures to third-year undergraduates in mathematics at Cambridge University, sufficient attention is given to theory to make it highly suitable as a mathematical textbook at undergraduate or postgraduate level.

Author : Narenda Govil,Ram N. Mohapatra,Zuhair Nashed,A. Sharma,J. Szabados
Publisher : CRC Press
Page : 551 pages
File Size : 48,5 Mb
Release : 2021-02-01
Category : Mathematics
ISBN : 9781000146035

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Approximation Theory by Narenda Govil,Ram N. Mohapatra,Zuhair Nashed,A. Sharma,J. Szabados Pdf

"Contains the contributions of 45 internationally distinguished mathematicians covering all areas of approximation theory-written in honor of the pioneering work of Arun K. Varma to the fields of interpolation and approximation of functions, including Birhoff interpolation and approximation by spline functions."

Author : Carl De Boor,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 152 pages
File Size : 45,6 Mb
Release : 1986-12-31
Category : Mathematics
ISBN : 0821867431

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Approximation Theory by Carl De Boor,American Mathematical Society Pdf

The papers in this book, first presented at a 1986 AMS Short Course, give a brief introduction to approximation theory and some of its current areas of active research, both theoretical and applied. The first lecture describes and illustrates the basic concerns of the field. Topics highlighted in the other lectures include the following: approximation in the complex domain, $N$-width, optimal recovery, interpolation, algorithms for approximation, and splines, with a strong emphasis on a multivariate setting for the last three topics. The book is aimed at mathematicians interested in an introduction to areas of current research and to engineers and scientists interested in exploring the field for possible applications to their own fields. The book is best understood by those with a standard first graduate course in real and complex analysis, but some of the presentations are accessible with the minimal requirements of advanced calculus and linear algebra.

Author : Ole Christensen,Khadija Laghrida Christensen
Publisher : Springer Science & Business Media
Page : 166 pages
File Size : 52,5 Mb
Release : 2012-11-04
Category : Mathematics
ISBN : 9780817644482

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Approximation Theory by Ole Christensen,Khadija Laghrida Christensen Pdf

This concisely written book gives an elementary introduction to a classical area of mathematics – approximation theory – in a way that naturally leads to the modern field of wavelets. The exposition, driven by ideas rather than technical details and proofs, demonstrates the dynamic nature of mathematics and the influence of classical disciplines on many areas of modern mathematics and applications. Featuring classical, illustrative examples and constructions, exercises, and a discussion of the role of wavelets to areas such as digital signal processing and data compression, the book is one of the few to describe wavelets in words rather than mathematical symbols.

Author : Hrushikesh Narhar Mhaskar,Devidas V. Pai
Publisher : Alpha Science International, Limited
Page : 572 pages
File Size : 47,8 Mb
Release : 2007
Category : Mathematics
ISBN : UCSC:32106019292199

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Fundamentals of Approximation Theory by Hrushikesh Narhar Mhaskar,Devidas V. Pai Pdf

This book presents a systematic and in-depth treatment of some basic topics in approximation theory in an effort to emphasize the rich connections of different branches of analysis with this subject. It contains a good blend of both the classical as well as abstract topics in the domain and their interconnections as appropriate. The approach is from the very concrete to more and more abstract levels. In order to provide a historical perspective on the results, a section on notes is appended to each chapter with an extensive bibliography. Researchers will find several references to recent developments. Problems of varying degree of difficulty accompany each chapter. Some of these problems complement certain results from the text. The others, more challenging, are drawn from the contemporary research articles. Ample hints are provided for such problems. Primarily aimed at graduate students and teachers of mathematics, researchers interested in an introduction to the specific results or techniques of approximation theory will find this book very attractive.

Author : Theodore J. Rivlin
Publisher : Courier Corporation
Page : 164 pages
File Size : 50,6 Mb
Release : 1981-01-01
Category : Mathematics
ISBN : 0486640698

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An Introduction to the Approximation of Functions by Theodore J. Rivlin Pdf

Mathematics of Computing -- Numerical Analysis.

Author : Marian Neamtu,Larry Schumaker
Publisher : Springer Science & Business Media
Page : 420 pages
File Size : 44,5 Mb
Release : 2011-11-19
Category : Mathematics
ISBN : 9781461407720

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Approximation Theory XIII: San Antonio 2010 by Marian Neamtu,Larry Schumaker Pdf

These proceedings were prepared in connection with the international conference Approximation Theory XIII, which was held March 7–10, 2010 in San Antonio, Texas. The conference was the thirteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 144 participants. Previous conferences in the series were held in Austin, Texas (1973, 1976, 1980, 1992), College Station, Texas (1983, 1986, 1989, 1995), Nashville, Tennessee (1998), St. Louis, Missouri (2001), Gatlinburg, Tennessee (2004), and San Antonio, Texas (2007). Along with the many plenary speakers, the contributors to this proceedings provided inspiring talks and set a high standard of exposition in their descriptions of new directions for research. Many relevant topics in approximation theory are included in this book, such as abstract approximation, approximation with constraints, interpolation and smoothing, wavelets and frames, shearlets, orthogonal polynomials, univariate and multivariate splines, and complex approximation.

Author : N. I. Achieser
Publisher : Courier Corporation
Page : 324 pages
File Size : 53,9 Mb
Release : 2013-06-05
Category : Mathematics
ISBN : 9780486153131

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Theory of Approximation by N. I. Achieser Pdf

A pioneer of many modern developments in approximation theory, N. I. Achieser designed this graduate-level text from the standpoint of functional analysis. The first two chapters address approximation problems in linear normalized spaces and the ideas of P. L. Tchebysheff. Chapter III examines the elements of harmonic analysis, and Chapter IV, integral transcendental functions of the exponential type. The final two chapters explore the best harmonic approximation of functions and Wiener's theorem on approximation. Professor Achieser concludes this exemplary text with an extensive section of problems and applications (elementary extremal problems, Szego's theorem, the Carathéodory-Fejér problem, and more).

Author : Elliott Ward Cheney
Publisher : Chelsea Publishing Company, Incorporated
Page : 280 pages
File Size : 52,5 Mb
Release : 1982
Category : Mathematics
ISBN : STANFORD:36105033183943

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Introduction to Approximation Theory by Elliott Ward Cheney Pdf

Author : G. A. Watson
Publisher : John Wiley & Sons
Page : 248 pages
File Size : 42,7 Mb
Release : 1980
Category : Mathematics
ISBN : UOM:39015015733853

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Approximation Theory and Numerical Methods by G. A. Watson Pdf

Author : Themistocles M. Rassias,Vijay Gupta
Publisher : Springer
Page : 741 pages
File Size : 42,6 Mb
Release : 2016-06-03
Category : Mathematics
ISBN : 9783319312811

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Mathematical Analysis, Approximation Theory and Their Applications by Themistocles M. Rassias,Vijay Gupta Pdf

Designed for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.

Author : E. W. Cheney
Publisher : SIAM
Page : 74 pages
File Size : 51,8 Mb
Release : 1986-01-01
Category : Mathematics
ISBN : 1611970199

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Multivariate Approximation Theory by E. W. Cheney Pdf

The approximation of functions of several variables continues to be a difficult problem in scientific computing because many of the algorithms required for such problems have yet to be written. This monograph is written for a broad audience of computational mathematicians and statisticians concerned with the development of algorithms or the derivation of approximations from linear projections, of which the interpolating operators are an important example. As an aid to both researchers and students, a bibliography of more than 200 titles is included.