An Introduction to the Approximation of Functions
Author: Theodore J. Rivlin
Publisher: Courier Corporation
Published: 1981-01-01
Total Pages: 164
ISBN-13: 9780486640693
DOWNLOAD EBOOKMathematics of Computing -- Numerical Analysis.
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Approximation Theory and Methods
Author: M. J. D. Powell
Publisher: Cambridge University Press
Published: 1981-03-31
Total Pages: 356
ISBN-13: 9780521295147
DOWNLOAD EBOOKMost 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.
Functional Analysis, Approximation Theory, and Numerical Analysis
Author: John Michael Rassias
Publisher: World Scientific
Published: 1994
Total Pages: 342
ISBN-13: 9789810207373
DOWNLOAD EBOOKThis book consists of papers written by outstanding mathematicians. It deals with both theoretical and applied aspects of the mathematical contributions of BANACH, ULAM, and OSTROWSKI, which broaden the horizons of Functional Analysis, Approximation Theory, and Numerical Analysis in accordance with contemporary mathematical standards.
Approximation Theory and Approximation Practice, Extended Edition
Author: Lloyd N. Trefethen
Publisher: SIAM
Published: 2019-01-01
Total Pages: 377
ISBN-13: 1611975948
DOWNLOAD EBOOKThis 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.
Approximation of Functions: Theory and Numerical Methods
Author: Günter Meinardus
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 207
ISBN-13: 3642856438
DOWNLOAD EBOOKfor example, the so-called Lp approximation, the Bernstein approxima tion problem (approximation on the real line by certain entire functions), and the highly interesting studies of J. L. WALSH on approximation in the complex plane. I would like to extend sincere thanks to Professor L. COLLATZ for his many encouragements for the writing of this book. Thanks are equally due to Springer-Verlag for their ready agreement to my wishes, and for the excellent and competent composition of the book. In addition, I would like to thank Dr. W. KRABS, Dr. A. -G. MEYER and D. SCHWEDT for their very careful reading of the manuscript. Hamburg, March 1964 GUNTER MEINARDUS Preface to the English Edition This English edition was translated by Dr. LARRY SCHUMAKER, Mathematics Research Center, United States Army, The University of Wisconsin, Madison, from a supplemented version of the German edition. Apart from a number of minor additions and corrections and a few new proofs (e. g. , the new proof of JACKSON'S Theorem), it differs in detail from the first edition by the inclusion of a discussion of new work on comparison theorems in the case of so-called regular Haar systems (§ 6) and on Segment Approximation (§ 11). I want to thank the many readers who provided comments and helpful suggestions. My special thanks are due to the translator, to Springer-Verlag for their ready compliance with all my wishes, to Mr.
Weighted Polynomial Approximation and Numerical Methods for Integral Equations
Author: Peter Junghanns
Publisher: Birkhäuser
Published: 2022-08-13
Total Pages: 0
ISBN-13: 9783030774998
DOWNLOAD EBOOKThe book presents a combination of two topics: one coming from the theory of approximation of functions and integrals by interpolation and quadrature, respectively, and the other from the numerical analysis of operator equations, in particular, of integral and related equations. The text focusses on interpolation and quadrature processes for functions defined on bounded and unbounded intervals and having certain singularities at the endpoints of the interval, as well as on numerical methods for Fredholm integral equations of first and second kind with smooth and weakly singular kernel functions, linear and nonlinear Cauchy singular integral equations, and hypersingular integral equations. The book includes both classic and very recent results and will appeal to graduate students and researchers who want to learn about the approximation of functions and the numerical solution of operator equations, in particular integral equations.
Numerical Approximation Methods
Author: Harold Cohen
Publisher: Springer Science & Business Media
Published: 2011-09-28
Total Pages: 493
ISBN-13: 1441998365
DOWNLOAD EBOOKThis 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.
Mathematical Analysis, Approximation Theory and Their Applications
Author: Themistocles M. Rassias
Publisher: Springer
Published: 2016-06-03
Total Pages: 745
ISBN-13: 3319312812
DOWNLOAD EBOOKDesigned for graduate students, researchers, and engineers in mathematics, optimization, and economics, this self-contained volume presents theory, methods, and applications in mathematical analysis and approximation theory. Specific topics include: approximation of functions by linear positive operators with applications to computer aided geometric design, numerical analysis, optimization theory, and solutions of differential equations. Recent and significant developments in approximation theory, special functions and q-calculus along with their applications to mathematics, engineering, and social sciences are discussed and analyzed. Each chapter enriches the understanding of current research problems and theories in pure and applied research.
Fourier Analysis and Approximation of Functions
Author: Roald M. Trigub
Publisher: Springer Science & Business Media
Published: 2004-09-07
Total Pages: 610
ISBN-13: 9781402023415
DOWNLOAD EBOOKIn Fourier Analysis and Approximation of Functions basics of classical Fourier Analysis are given as well as those of approximation by polynomials, splines and entire functions of exponential type. In Chapter 1 which has an introductory nature, theorems on convergence, in that or another sense, of integral operators are given. In Chapter 2 basic properties of simple and multiple Fourier series are discussed, while in Chapter 3 those of Fourier integrals are studied. The first three chapters as well as partially Chapter 4 and classical Wiener, Bochner, Bernstein, Khintchin, and Beurling theorems in Chapter 6 might be interesting and available to all familiar with fundamentals of integration theory and elements of Complex Analysis and Operator Theory. Applied mathematicians interested in harmonic analysis and/or numerical methods based on ideas of Approximation Theory are among them. In Chapters 6-11 very recent results are sometimes given in certain directions. Many of these results have never appeared as a book or certain consistent part of a book and can be found only in periodics; looking for them in numerous journals might be quite onerous, thus this book may work as a reference source. The methods used in the book are those of classical analysis, Fourier Analysis in finite-dimensional Euclidean space Diophantine Analysis, and random choice.
Computer Aided Geometric Design
Author: Robert E. Barnhill
Publisher: Academic Press
Published: 2014-05-10
Total Pages: 337
ISBN-13: 1483268489
DOWNLOAD EBOOKComputer Aided Geometric Design covers the proceedings of the First International Conference on Computer Aided Geometric Design, held at the University of Utah on March 18-21, 1974. This book is composed of 15 chapters and starts with reviews of the properties of surface patch equation and the use of computers in geometrical design. The next chapters deal with the principles of smooth interpolation over triangles and without twist constraints, as well as the graphical representation of surfaces over triangles and rectangles. These topics are followed by discussions of the B-spline curves and surfaces; mathematical and practical possibilities of UNISURF; nonlinear splines; and some piecewise polynomial alternatives to splines under tension. Other chapters explore the smooth parametric surfaces, the space curve as a folded edge, and the interactive computer graphics application of the parametric bi-cubic surface to engineering design problems. The final chapters look into the three-dimensional human-machine communication and a class of local interpolating splines. This book will prove useful to design engineers.
