Approximation Theory And Approximation Practice Extended Edition

Author : Lloyd N. Trefethen
Publisher : SIAM
Page : 375 pages
File Size : 49,6 Mb
Release : 2019-01-01
Category : Mathematics
ISBN : 9781611975949

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Approximation Theory and Approximation Practice, Extended Edition by Lloyd N. Trefethen Pdf

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 field’s 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 : Theodore J. Rivlin
Publisher : Courier Corporation
Page : 164 pages
File Size : 47,8 Mb
Release : 1981-01-01
Category : Mathematics
ISBN : 0486640698

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An Introduction to the Approximation of Functions by Theodore J. Rivlin Pdf

Mathematics of Computing -- Numerical Analysis.

Author : M. J. D. Powell
Publisher : Cambridge University Press
Page : 356 pages
File Size : 55,8 Mb
Release : 1981-03-31
Category : Mathematics
ISBN : 0521295149

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Approximation Theory and Methods by M. J. D. Powell Pdf

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 : Elliott Ward Cheney,William Allan Light
Publisher : American Mathematical Soc.
Page : 379 pages
File Size : 47,7 Mb
Release : 2009-01-13
Category : Mathematics
ISBN : 9780821847985

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A Course in Approximation Theory by Elliott Ward Cheney,William Allan Light Pdf

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 : Narenda Govil,Ram N. Mohapatra,Zuhair Nashed,A. Sharma,J. Szabados
Publisher : CRC Press
Page : 551 pages
File Size : 52,6 Mb
Release : 2021-02-01
Category : Mathematics
ISBN : 9781000146035

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Approximation Theory by Narenda Govil,Ram N. Mohapatra,Zuhair Nashed,A. Sharma,J. Szabados Pdf

"Contains the contributions of 45 internationally distinguished mathematicians covering all areas of approximation theory-written in honor of the pioneering work of Arun K. Varma to the fields of interpolation and approximation of functions, including Birhoff interpolation and approximation by spline functions."

Author : Carl De Boor,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 152 pages
File Size : 41,6 Mb
Release : 1986-12-31
Category : Mathematics
ISBN : 0821867431

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Approximation Theory by Carl De Boor,American Mathematical Society Pdf

The papers in this book, first presented at a 1986 AMS Short Course, give a brief introduction to approximation theory and some of its current areas of active research, both theoretical and applied. The first lecture describes and illustrates the basic concerns of the field. Topics highlighted in the other lectures include the following: approximation in the complex domain, $N$-width, optimal recovery, interpolation, algorithms for approximation, and splines, with a strong emphasis on a multivariate setting for the last three topics. The book is aimed at mathematicians interested in an introduction to areas of current research and to engineers and scientists interested in exploring the field for possible applications to their own fields. The book is best understood by those with a standard first graduate course in real and complex analysis, but some of the presentations are accessible with the minimal requirements of advanced calculus and linear algebra.

Author : Harold S. Shapiro
Publisher : Springer
Page : 283 pages
File Size : 46,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540364979

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Topics in Approximation Theory by Harold S. Shapiro Pdf

Author : N. I. Achieser
Publisher : Courier Corporation
Page : 324 pages
File Size : 46,6 Mb
Release : 2013-06-05
Category : Mathematics
ISBN : 9780486153131

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Theory of Approximation by N. I. Achieser Pdf

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).

Author : G. A. Watson
Publisher : John Wiley & Sons
Page : 248 pages
File Size : 42,7 Mb
Release : 1980
Category : Mathematics
ISBN : UOM:39015015733853

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Approximation Theory and Numerical Methods by G. A. Watson Pdf

Author : Theodore J. Rivlin
Publisher : Wiley-Interscience
Page : 200 pages
File Size : 54,9 Mb
Release : 1974
Category : Mathematics
ISBN : MINN:319510004728748

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The Chebyshev Polynomials by Theodore J. Rivlin Pdf

Author : Ole Christensen,Khadija Laghrida Christensen
Publisher : Springer Science & Business Media
Page : 166 pages
File Size : 46,9 Mb
Release : 2012-11-04
Category : Mathematics
ISBN : 9780817644482

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Approximation Theory by Ole Christensen,Khadija Laghrida Christensen Pdf

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 : Hrushikesh Narhar Mhaskar,Devidas V. Pai
Publisher : CRC Press
Page : 580 pages
File Size : 41,6 Mb
Release : 2000
Category : Mathematics
ISBN : 0849309395

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Fundamentals of Approximation Theory by Hrushikesh Narhar Mhaskar,Devidas V. Pai Pdf

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 : Nikolaĭ Pavlovich Korneĭchuk
Publisher : Cambridge University Press
Page : 472 pages
File Size : 52,7 Mb
Release : 1991-06-06
Category : Mathematics
ISBN : 0521382343

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Exact Constants in Approximation Theory by Nikolaĭ Pavlovich Korneĭchuk Pdf

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 : Themistocles M. Rassias,Vijay Gupta
Publisher : Springer
Page : 741 pages
File Size : 53,7 Mb
Release : 2016-06-03
Category : Mathematics
ISBN : 9783319312811

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Mathematical Analysis, Approximation Theory and Their Applications by Themistocles M. Rassias,Vijay Gupta Pdf

Designed 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.

Author : Maurizio Falcone,Roberto Ferretti
Publisher : SIAM
Page : 331 pages
File Size : 55,8 Mb
Release : 2014-01-31
Category : Mathematics
ISBN : 9781611973044

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Semi-Lagrangian Approximation Schemes for Linear and Hamilton-Jacobi Equations by Maurizio Falcone,Roberto Ferretti Pdf

This largely self-contained book provides a unified framework of semi-Lagrangian strategy for the approximation of hyperbolic PDEs, with a special focus on Hamilton-Jacobi equations. The authors provide a rigorous discussion of the theory of viscosity solutions and the concepts underlying the construction and analysis of difference schemes; they then proceed to high-order semi-Lagrangian schemes and their applications to problems in fluid dynamics, front propagation, optimal control, and image processing. The developments covered in the text and the references come from a wide range of literature.