A Course In Approximation Theory

Author : Elliott Ward Cheney,William Allan Light
Publisher : American Mathematical Soc.
Page : 379 pages
File Size : 44,7 Mb
Release : 2009-01-13
Category : Mathematics
ISBN : 9780821847985

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A Course in Approximation Theory by Elliott Ward Cheney,William Allan Light Pdf

This textbook is designed for graduate students in mathematics, physics, engineering, and computer science. Its purpose is to guide the reader in exploring contemporary approximation theory. The emphasis is on multi-variable approximation theory, i.e., the approximation of functions in several variables, as opposed to the classical theory of functions in one variable. Most of the topics in the book, heretofore accessible only through research papers, are treated here from the basics to the currently active research, often motivated by practical problems arising in diverse applications such as science, engineering, geophysics, and business and economics. Among these topics are projections, interpolation paradigms, positive definite functions, interpolation theorems of Schoenberg and Micchelli, tomography, artificial neural networks, wavelets, thin-plate splines, box splines, ridge functions, and convolutions. An important and valuable feature of the book is the bibliography of almost 600 items directing the reader to important books and research papers. There are 438 problems and exercises scattered through the book allowing the student reader to get a better understanding of the subject.

Author : Ward Cheney,Will Light
Publisher : Unknown
Page : 128 pages
File Size : 54,7 Mb
Release : 2024-06-30
Category : Electronic
ISBN : 9812652612

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A Course In Approximation Theory by Ward Cheney,Will Light Pdf

Author : M. J. D. Powell
Publisher : Cambridge University Press
Page : 356 pages
File Size : 45,8 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 : W.·谢尼,W.·莱特
Publisher : Unknown
Page : 357 pages
File Size : 41,9 Mb
Release : 2004
Category : Approximation theory
ISBN : 7111135121

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逼近论教程 by W.·谢尼,W.·莱特 Pdf

责任者译名:谢尼。

Author : Armin Iske
Publisher : Springer
Page : 358 pages
File Size : 52,6 Mb
Release : 2018-12-14
Category : Mathematics
ISBN : 9783030052287

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Approximation Theory and Algorithms for Data Analysis by Armin Iske Pdf

This textbook offers an accessible introduction to the theory and numerics of approximation methods, combining classical topics of approximation with recent advances in mathematical signal processing, and adopting a constructive approach, in which the development of numerical algorithms for data analysis plays an important role. The following topics are covered: * least-squares approximation and regularization methods * interpolation by algebraic and trigonometric polynomials * basic results on best approximations * Euclidean approximation * Chebyshev approximation * asymptotic concepts: error estimates and convergence rates * signal approximation by Fourier and wavelet methods * kernel-based multivariate approximation * approximation methods in computerized tomography Providing numerous supporting examples, graphical illustrations, and carefully selected exercises, this textbook is suitable for introductory courses, seminars, and distance learning programs on approximation for undergraduate students.

Author : Lloyd N. Trefethen
Publisher : SIAM
Page : 375 pages
File Size : 49,6 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 : Carl De Boor,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 152 pages
File Size : 55,9 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 : Hrushikesh Narhar Mhaskar,Devidas V. Pai
Publisher : CRC Press
Page : 580 pages
File Size : 45,8 Mb
Release : 2000
Category : Mathematics
ISBN : 0849309395

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

The field of approximation theory has become so vast that it intersects with every other branch of analysis and plays an increasingly important role in applications in the applied sciences and engineering. Fundamentals of Approximation Theory presents a systematic, in-depth treatment of some basic topics in approximation theory designed to emphasize the rich connections of the subject with other areas of study. With an approach that moves smoothly from the very concrete to more and more abstract levels, this text provides an outstanding blend of classical and abstract topics. The first five chapters present the core of information that readers need to begin research in this domain. The final three chapters the authors devote to special topics-splined functions, orthogonal polynomials, and best approximation in normed linear spaces- that illustrate how the core material applies in other contexts and expose readers to the use of complex analytic methods in approximation theory. Each chapter contains problems of varying difficulty, including some drawn from contemporary research. Perfect for an introductory graduate-level class, Fundamentals of Approximation Theory also contains enough advanced material to serve more specialized courses at the doctoral level and to interest scientists and engineers.

Author : George M. Phillips
Publisher : Springer Science & Business Media
Page : 325 pages
File Size : 41,7 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387216829

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Interpolation and Approximation by Polynomials by George M. Phillips Pdf

In addition to coverage of univariate interpolation and approximation, the text includes material on multivariate interpolation and multivariate numerical integration, a generalization of the Bernstein polynomials that has not previously appeared in book form, and a greater coverage of Peano kernel theory than is found in most textbooks. There are many worked examples and each section ends with a number of carefully selected problems that extend the student's understanding of the text. The author is well known for his clarity of writing and his many contributions as a researcher in approximation theory.

Author : Theodore J. Rivlin
Publisher : Courier Corporation
Page : 164 pages
File Size : 42,6 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 : Harold S. Shapiro
Publisher : Springer
Page : 283 pages
File Size : 47,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540364979

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Topics in Approximation Theory by Harold S. Shapiro Pdf

Author : Leopoldo Nachbin
Publisher : Unknown
Page : 140 pages
File Size : 45,5 Mb
Release : 1967
Category : Approximation theory
ISBN : UOM:39015001319956

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Elements of Approximation Theory by Leopoldo Nachbin Pdf

Author : H N Mhaskar
Publisher : World Scientific
Page : 396 pages
File Size : 48,9 Mb
Release : 1997-01-04
Category : Mathematics
ISBN : 9789814518055

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Introduction To The Theory Of Weighted Polynomial Approximation by H N Mhaskar Pdf

In this book, we have attempted to explain a variety of different techniques and ideas which have contributed to this subject in its course of successive refinements during the last 25 years. There are other books and surveys reviewing the ideas from the perspective of either potential theory or orthogonal polynomials. The main thrust of this book is to introduce the subject from an approximation theory point of view. Thus, the main motivation is to study analogues of results from classical trigonometric approximation theory, introducing other ideas as needed. It is not our objective to survey the most recent results, but merely to introduce to the readers the thought processes and ideas as they are developed.This book is intended to be self-contained, although the reader is expected to be familiar with rudimentary real and complex analysis. It will also help to have studied elementary trigonometric approximation theory, and have some exposure to orthogonal polynomials.

Author : C. K. Chui,Larry L. Schumaker
Publisher : World Scientific
Page : 454 pages
File Size : 46,6 Mb
Release : 1995
Category : Mathematics
ISBN : 9789814532600

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Approximation Theory Eight by C. K. Chui,Larry L. Schumaker Pdf

This is the collection of the refereed and edited papers presented at the 8th Texas International Conference on Approximation Theory. It is interdisciplinary in nature and consists of two volumes. The central theme of Vol. I is the core of approximation theory. It includes such important areas as qualitative approximations, interpolation theory, rational approximations, radial-basis functions, and splines. The second volume focuses on topics related to wavelet analysis, including multiresolution and multi-level approximation, subdivision schemes in CAGD, and applications.

Author : Karl-Georg Steffens
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 43,9 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