The Theory Of Approximation
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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.
The Theory Of Approximation
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Author : Dunham Jackson
language : en
Publisher: American Mathematical Soc.
Release Date : 1930-12-31
The Theory Of Approximation written by Dunham Jackson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1930-12-31 with Mathematics categories.
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 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.
Theory Of Approximation
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Author : N. I. Achieser
language : en
Publisher: Courier Corporation
Release Date : 2013-06-05
Theory Of Approximation written by N. I. Achieser and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-05 with Mathematics categories.
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).
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.
The History Of Approximation Theory
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Author : Karl-Georg Steffens
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-28
The History Of Approximation Theory written by Karl-Georg Steffens 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 2007-07-28 with Mathematics categories.
* 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
Fundamentals Of Approximation Theory
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Author : Hrushikesh Narhar Mhaskar
language : en
Publisher: CRC Press
Release Date : 2000
Fundamentals Of Approximation Theory written by Hrushikesh Narhar Mhaskar and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
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.
Introduction To The Theory Of Weighted Polynomial Approximation
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Author : Hrushikesh Narhar Mhaskar
language : en
Publisher: World Scientific
Release Date : 1996
Introduction To The Theory Of Weighted Polynomial Approximation written by Hrushikesh Narhar Mhaskar and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
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.
Nonlinear Approximation Theory
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Author : Dietrich Braess
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Nonlinear Approximation Theory written by Dietrich Braess 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 2012-12-06 with Mathematics categories.
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 branchesof 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.