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Author : Elliott Ward Cheney
Publisher : Chelsea Publishing Company, Incorporated
Page : 280 pages
File Size : 54,9 Mb
Release : 1982
Category : Mathematics
ISBN : STANFORD:36105033183943
Author : Theodore J. Rivlin
Publisher : Courier Corporation
Page : 164 pages
File Size : 50,6 Mb
Release : 1981-01-01
Category : Mathematics
ISBN : 0486640698
Mathematics of Computing -- Numerical Analysis.
Author : Ole Christensen,Khadija Laghrida Christensen
Publisher : Springer Science & Business Media
Page : 166 pages
File Size : 45,5 Mb
Release : 2012-11-04
Category : Mathematics
ISBN : 9780817644482
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 : Elliott Ward Cheney,William Allan Light
Publisher : American Mathematical Soc.
Page : 379 pages
File Size : 42,6 Mb
Release : 2009-01-13
Category : Mathematics
ISBN : 9780821847985
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 : M. J. D. Powell
Publisher : Cambridge University Press
Page : 356 pages
File Size : 45,7 Mb
Release : 1981-03-31
Category : Mathematics
ISBN : 0521295149
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 : Lloyd N. Trefethen
Publisher : SIAM
Page : 375 pages
File Size : 52,9 Mb
Release : 2019-01-01
Category : Mathematics
ISBN : 9781611975949
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 : H N Mhaskar
Publisher : World Scientific
Page : 396 pages
File Size : 52,8 Mb
Release : 1997-01-04
Category : Mathematics
ISBN : 9789814518055
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 : Karl-Georg Steffens
Publisher : Springer Science & Business Media
Page : 219 pages
File Size : 49,9 Mb
Release : 2007-07-28
Category : Mathematics
ISBN : 9780817644758
* 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 : Armin Iske
Publisher : Springer
Page : 358 pages
File Size : 52,5 Mb
Release : 2018-12-14
Category : Mathematics
ISBN : 9783030052287
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 : Carl De Boor
Publisher : American Mathematical Soc.
Page : 145 pages
File Size : 48,8 Mb
Release : 1986
Category : Mathematics
ISBN : 9780821800980
Presented at a 1986 AMS Short Course, this title contains papers that give a brief introduction to approximation theory and some of its areas of active research, both theoretical and applied. It is best understood by those with a standard first graduate course in real and complex analysis.
Author : Nikolaĭ Pavlovich Korneĭchuk
Publisher : Cambridge University Press
Page : 472 pages
File Size : 47,9 Mb
Release : 1991-06-06
Category : Mathematics
ISBN : 0521382343
This book is intended as a self-contained introduction for non-specialists, or as a reference work for experts, to the particular area of approximation theory that is concerned with exact constants. The results apply mainly to extremal problems in approximation theory, which in turn are closely related to numerical analysis and optimization. The book encompasses a wide range of questions and problems: best approximation by polynomials and splines; linear approximation methods, such as spline-approximation; optimal reconstruction of functions and linear functionals. Many of the results are based on deep facts from analysis and function theory, such as duality theory and comparison theorems; these are presented in chapters 1 and 3. In keeping with the author's intention to make the book as self-contained as possible, chapter 2 contains an introduction to polynomial and spline approximation. Chapters 4 to 7 apply the theory to specific classes of functions. The last chapter deals with n-widths and generalises some of the ideas of the earlier chapters. Each chapter concludes with commentary, exercises and extensions of results. A substantial bibliography is included. Many of the results collected here have not been gathered together in book form before, so it will be essential reading for approximation theorists.
Author : Dunham Jackson
Publisher : American Mathematical Soc.
Page : 186 pages
File Size : 50,9 Mb
Release : 1930-12-31
Category : Numerical analysis
ISBN : 9780821838921
Author : Hrushikesh Narhar Mhaskar,Devidas V. Pai
Publisher : CRC Press
Page : 580 pages
File Size : 45,7 Mb
Release : 2000
Category : Mathematics
ISBN : 0849309395
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 : Felipe Cucker,Ding Xuan Zhou
Publisher : Cambridge University Press
Page : 128 pages
File Size : 55,5 Mb
Release : 2007-03-29
Category : Computers
ISBN : 9781139462860
The goal of learning theory is to approximate a function from sample values. To attain this goal learning theory draws on a variety of diverse subjects, specifically statistics, approximation theory, and algorithmics. Ideas from all these areas blended to form a subject whose many successful applications have triggered a rapid growth during the last two decades. This is the first book to give a general overview of the theoretical foundations of the subject emphasizing the approximation theory, while still giving a balanced overview. It is based on courses taught by the authors, and is reasonably self-contained so will appeal to a broad spectrum of researchers in learning theory and adjacent fields. It will also serve as an introduction for graduate students and others entering the field, who wish to see how the problems raised in learning theory relate to other disciplines.
Author : Harold S. Shapiro
Publisher : Springer
Page : 283 pages
File Size : 55,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540364979