Methods Of Approximation Theory
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Approximation Theory And Methods
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Author : M. J. D. Powell
language : en
Publisher: Cambridge University Press
Release Date : 1981-03-31
Approximation Theory And Methods written by M. J. D. Powell and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-03-31 with Mathematics categories.
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.
Approximation Theory And Algorithms For Data Analysis
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Author : Armin Iske
language : en
Publisher: Springer
Release Date : 2018-12-14
Approximation Theory And Algorithms For Data Analysis written by Armin Iske and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-14 with Mathematics categories.
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.
Approximation Theory And Numerical Methods
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Author : G. A. Watson
language : en
Publisher: John Wiley & Sons
Release Date : 1980
Approximation Theory And Numerical Methods written by G. A. Watson and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.
An Introduction To The Approximation Of Functions
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Author : Theodore J. Rivlin
language : en
Publisher: Courier Corporation
Release Date : 1981-01-01
An Introduction To The Approximation Of Functions written by Theodore J. Rivlin and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-01-01 with Mathematics categories.
Mathematics of Computing -- Numerical Analysis.
Methods Of Approximation Theory
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Author : Alexander I. Stepanets
language : en
Publisher: Walter de Gruyter
Release Date : 2011-12-22
Methods Of Approximation Theory written by Alexander I. Stepanets and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-22 with Mathematics categories.
No detailed description available for "Methods of Approximation Theory".
Approximation Theory And Approximation Practice Extended Edition
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Author : Lloyd N. Trefethen
language : en
Publisher: SIAM
Release Date : 2019-01-01
Approximation Theory And Approximation Practice Extended Edition written by Lloyd N. Trefethen and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-01 with Mathematics categories.
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.
Exact Constants In Approximation Theory
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Author : Nikolaĭ Pavlovich Korneĭchuk
language : en
Publisher: Cambridge University Press
Release Date : 1991-06-06
Exact Constants In Approximation Theory written by Nikolaĭ Pavlovich Korneĭchuk and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-06-06 with Mathematics categories.
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.
Numerical Approximation Methods
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Author : Harold Cohen
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-09-28
Numerical Approximation Methods written by Harold Cohen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-28 with Mathematics categories.
This book presents numerical and other approximation techniques for solving various types of mathematical problems that cannot be solved analytically. In addition to well known methods, it contains some non-standard approximation techniques that are now formally collected as well as original methods developed by the author that do not appear in the literature. This book contains an extensive treatment of approximate solutions to various types of integral equations, a topic that is not often discussed in detail. There are detailed analyses of ordinary and partial differential equations and descriptions of methods for estimating the values of integrals that are presented in a level of detail that will suggest techniques that will be useful for developing methods for approximating solutions to problems outside of this text. The book is intended for researchers who must approximate solutions to problems that cannot be solved analytically. It is also appropriate for students taking courses in numerical approximation techniques.