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Author | : M. J. D. Powell |
Publisher | : Cambridge University Press |
Total Pages | : 356 |
Release | : 1981-03-31 |
Genre | : Mathematics |
ISBN | : 9780521295147 |
Download Approximation Theory and Methods Book in PDF, ePub and Kindle
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 | : Lloyd N. Trefethen |
Publisher | : SIAM |
Total Pages | : 375 |
Release | : 2019-01-01 |
Genre | : Mathematics |
ISBN | : 1611975948 |
Download Approximation Theory and Approximation Practice, Extended Edition Book in PDF, ePub and Kindle
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.
Author | : Hrushikesh Narhar Mhaskar |
Publisher | : CRC Press |
Total Pages | : 580 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 9780849309397 |
Download Fundamentals of Approximation Theory Book in PDF, ePub and Kindle
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 | : Themistocles M. Rassias |
Publisher | : Springer |
Total Pages | : 745 |
Release | : 2016-06-03 |
Genre | : Mathematics |
ISBN | : 3319312812 |
Download Mathematical Analysis, Approximation Theory and Their Applications Book in PDF, ePub and Kindle
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 | : Carl De Boor |
Publisher | : American Mathematical Soc. |
Total Pages | : 145 |
Release | : 1986 |
Genre | : Mathematics |
ISBN | : 0821800981 |
Download Approximation Theory Book in PDF, ePub and Kindle
Presented at a 1986 AMS Short Course, this title contains papers that give a brief introduction to approximation theory and some of its areas of active research, both theoretical and applied. It is best understood by those with a standard first graduate course in real and complex analysis.
Author | : Theodore J. Rivlin |
Publisher | : Courier Corporation |
Total Pages | : 164 |
Release | : 1981-01-01 |
Genre | : Mathematics |
ISBN | : 9780486640693 |
Download An Introduction to the Approximation of Functions Book in PDF, ePub and Kindle
Mathematics of Computing -- Numerical Analysis.
Author | : Charles K. Chui |
Publisher | : |
Total Pages | : |
Release | : |
Genre | : |
ISBN | : |
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Author | : H N Mhaskar |
Publisher | : World Scientific |
Total Pages | : 398 |
Release | : 1997-01-04 |
Genre | : Mathematics |
ISBN | : 9814518050 |
Download Introduction To The Theory Of Weighted Polynomial Approximation Book in PDF, ePub and Kindle
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.
Author | : George A. Anastassiou |
Publisher | : Springer Science & Business Media |
Total Pages | : 520 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461213606 |
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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.
Author | : Ole Christensen |
Publisher | : Springer Science & Business Media |
Total Pages | : 166 |
Release | : 2012-11-04 |
Genre | : Mathematics |
ISBN | : 0817644482 |
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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.