Approximation Theory And Methods

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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 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.

Numerical Methods Of Approximation Theory

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Author : Lothar Collatz
language : en
Publisher:
Release Date : 1982

Numerical Methods Of Approximation Theory written by Lothar Collatz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with categories.

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.

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".

Methods Of Functional Analysis In Approximation Theory

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Author : Charles A. Micchelli
language : en
Publisher:
Release Date : 1986

Methods Of Functional Analysis In Approximation Theory written by Charles A. Micchelli and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.

Numerical Methods In Approximation Theory Vol 9

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Author : D. Braess
language : en
Publisher: Birkhäuser
Release Date : 2013-03-11

Numerical Methods In Approximation Theory Vol 9 written by D. Braess and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-11 with Social Science categories.

This book is the official proceedings of a conference on Numerical Methods in Approximation Theory which was held at the Mathematisches Forschungs institut in Oberwolfach during the week of November 24~30, 1991. It contains refereed and edited papers by 20 of the 49 participants. The book is dedicated to the memory of Prof. Lothar Collatz who main tained a long and active interest in numerical approximation. It is the ninth in a series of volumes published by Birkhiiuser resulting from conferences on the subject held at Oberwolfach, and co-organized by Prof. Collatz. We now briefly describe the contents of the book. The paper of BASZEN SKI, DELVOS and JESTER deals with blending using sine double series expan sions of functions defined on the unit square. In addition to giving explicit error estimates for partial sums and for interpolating sine polynomials, they also show that Boolean sums yield almost the same asymptotic error estimates as the conventional tensor-product approach, but with a reduced number of terms. The paper of BEATSON and LIGHT discusses approximation by quasi interpolants which are sums of scaled translates of a one-parameter family of functions. They do not require reproduction of low degree polynomials, but nevertheless are able to give error bounds and analyze quasi-interpolation based on Gaussians and exponentials. BINEV and JETTER deal with multivariate interpolation using shifts of a single basis function. They treat both gridded data and scattered data. As examples, they consider box splines and certain radial basis functions.

Complex Methods In Approximation Theory

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Author : Francisco Marcellán
language : en
Publisher: Universidad Almería
Release Date : 1997-01-01

Complex Methods In Approximation Theory written by Francisco Marcellán and has been published by Universidad Almería this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-01 with Mathematics categories.

This book provides an up-to-date account of research in Approximation Theory and Complex Analysis, areas which are the subject of recent exciting developments.The level of presentation should be suitable for anyone with a good knowledge of analysis, including scientists with a mathematical background. The volume contains both research papers and surveys, presented by specialists in the field. The areas discussed are: Orthogonal Polynomials (with respect to classical and Sobolev inner products), Approximation in Several Complex Variables, Korovkin-type Theorems, Potential Theory, Ratinal Approximation and Linear Ordinary Differential Equations.

Approximation Theory

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Author : George A. Anastassiou
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Approximation Theory written by George A. Anastassiou 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.

We study in Part I of this monograph the computational aspect of almost all moduli of continuity over wide classes of functions exploiting some of their convexity properties. To our knowledge it is the first time the entire calculus of moduli of smoothness has been included in a book. We then present numerous applications of Approximation Theory, giving exact val ues of errors in explicit forms. The K-functional method is systematically avoided since it produces nonexplicit constants. All other related books so far have allocated very little space to the computational aspect of moduli of smoothness. In Part II, we study/examine the Global Smoothness Preservation Prop erty (GSPP) for almost all known linear approximation operators of ap proximation theory including: trigonometric operators and algebraic in terpolation operators of Lagrange, Hermite-Fejer and Shepard type, also operators of stochastic type, convolution type, wavelet type integral opera tors and singular integral operators, etc. We present also a sufficient general theory for GSPP to hold true. We provide a great variety of applications of GSPP to Approximation Theory and many other fields of mathemat ics such as Functional analysis, and outside of mathematics, fields such as computer-aided geometric design (CAGD). Most of the time GSPP meth ods are optimal. Various moduli of smoothness are intensively involved in Part II. Therefore, methods from Part I can be used to calculate exactly the error of global smoothness preservation. It is the first time in the literature that a book has studied GSPP.

Approximation Theory And Approximation Practice

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Author : Lloyd N. Trefethen
language : en
Publisher: SIAM
Release Date : 2013-01-03

Approximation Theory And Approximation Practice 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 2013-01-03 with Mathematics categories.

An original and modern treatment of approximation theory for students in applied mathematics. Includes exercises, illustrations and Matlab code.