Download or read book An Introduction to the Approximation of Functions written by Theodore J. Rivlin and published by Courier Corporation. This book was released on 1981-01-01 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- Numerical Analysis.
Download or read book Approximation of Functions written by G. G. Lorentz and published by American Mathematical Soc.. This book was released on 2005 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an easily accessible book on the approximation of functions--simple and without unnecessary details, but complete enough to include the main results of the theory. Except for a few sections, only functions of a real variable are treated. This work can be used as a textbook for graduate or advanced undergraduate courses or for self-study. Included in the volume are Notes at the end of each chapter, Problems, and a selected Bibliography.
Download or read book Rational Approximation of Real Functions written by P. P. Petrushev and published by Cambridge University Press. This book was released on 2011-03-03 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 1987 book examines the approximation of real functions by real rational functions. These are a more convenient tool than polynomials, and interest in them was growing, especially after D. Newman's work in the mid-sixties. The authors present the basic achievements of the subject and also discuss some topics from complex rational approximation.
Download or read book Fourier Analysis and Approximation of Functions written by Roald M. Trigub and published by Springer Science & Business Media. This book was released on 2004-09-07 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 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.
Download or read book Theory of Uniform Approximation of Functions by Polynomials written by Vladislav K. Dzyadyk and published by Walter de Gruyter. This book was released on 2008-09-25 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough, self-contained and easily accessible treatment of the theory on the polynomial best approximation of functions with respect to maximum norms. The topics include Chebychev theory, Weierstraß theorems, smoothness of functions, and continuation of functions.
Download or read book Approximation Theory and Methods written by M. J. D. Powell and published by Cambridge University Press. This book was released on 1981-03-31 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Approximation Theory and Approximation Practice Extended Edition written by Lloyd N. Trefethen and published by SIAM. This book was released on 2019-01-01 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Theory of Approximation of Functions of a Real Variable written by A. F. Timan and published by Elsevier. This book was released on 2014-07-22 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Approximation of Functions of a Real Variable discusses a number of fundamental parts of the modern theory of approximation of functions of a real variable. The material is grouped around the problem of the connection between the best approximation of functions to their structural properties. This text is composed of eight chapters that highlight the relationship between the various structural properties of real functions and the character of possible approximations to them by polynomials and other functions of simple construction. Each chapter concludes with a section containing various problems and theorems, which supplement the main text. The first chapters tackle the Weierstrass's theorem, the best approximation by polynomials on a finite segment, and some compact classes of functions and their structural properties. The subsequent chapters describe some properties of algebraic polynomials and transcendental integral functions of exponential type, as well as the direct theorems of the constructive theory of functions. These topics are followed by discussions of differential and constructive characteristics of converse theorems. The final chapters explore other theorems connecting the best approximations functions with their structural properties. These chapters also deal with the linear processes of approximation of functions by polynomials. The book is intended for post-graduate students and for mathematical students taking advanced courses, as well as to workers in the field of the theory of functions.
Download or read book Interpolation and Approximation written by Philip J. Davis and published by Courier Corporation. This book was released on 1975-01-01 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intermediate-level survey covers remainder theory, convergence theorems, and uniform and best approximation. Other topics include least square approximation, Hilbert space, orthogonal polynomials, theory of closure and completeness, and more. 1963 edition.
Download or read book Analytic Number Theory Approximation Theory and Special Functions written by Gradimir V. Milovanović and published by Springer. This book was released on 2014-07-08 with total page 873 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, in honor of Hari M. Srivastava, discusses essential developments in mathematical research in a variety of problems. It contains thirty-five articles, written by eminent scientists from the international mathematical community, including both research and survey works. Subjects covered include analytic number theory, combinatorics, special sequences of numbers and polynomials, analytic inequalities and applications, approximation of functions and quadratures, orthogonality and special and complex functions. The mathematical results and open problems discussed in this book are presented in a simple and self-contained manner. The book contains an overview of old and new results, methods, and theories toward the solution of longstanding problems in a wide scientific field, as well as new results in rapidly progressing areas of research. The book will be useful for researchers and graduate students in the fields of mathematics, physics and other computational and applied sciences.
Download or read book A Course in Approximation Theory written by Elliott Ward Cheney and published by American Mathematical Soc.. This book was released on 2009-01-13 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Sparse Polynomial Approximation of High Dimensional Functions written by Ben Adcock and published by Society for Industrial and Applied Mathematics (SIAM). This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is a book about polynomial approximation in high dimensions"--
Download or read book Numerical Methods III Approximation of Functions written by Boris Obsieger and published by university-books.eu. This book was released on 2013-10-25 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is written primarily for the students on technical universities, but also as a useful handbook for engineers and PhD students. It introduces reader into various types of approximations of functions, which are defined either explicitly or by their values in the distinct set of points, as well as into economisation of existing approximation formulas. Why the approximation of functions is so important? Simply because various functions cannot be calculated without approximation. Approximation formulas for some of these functions (such as trigonometric functions and logarithms) are already implemented in the calculators and standard computer libraries, providing the precision to all bits of memory in which a value is stored. So high precision is not usually required in the engineering practice, and use more numerical operations that is really necessary. Economised approximation formulas can provide required precision with less numerical operation, and can made numerical algorithms faster, especially when such formulas are used in nested loops. The other important use of approximation is in calculating functions that are defined by values in the chosen set of points, such as in solving integral equations (usually obtained from differential equations). The book is divided into five chapters. In the first chapter are briefly explained basic principles of approximations, i.e. approximations near the chosen point (by Maclaurin, Taylor or Padé expansion), principles of approximations with orthogonal series and principles of least squares approximations. In the second chapter, various types of least squares polynomial approximations, particularly those by using orthogonal polynomials such as Legendre, Jacobi, Laguerre, Hermite, Zernike and Gram polynomials are explained. Third chapter explains approximations with Fourier series, which are the base for developing approximations with Chebyshev polynomials (fourth chapter). Uniform approximation and further usage of Chebyshev polynomials in the almost uniform approximation, as well as in economisation of existing approximation formulas, are described in fifth chapter. Practical applications of described approximation procedures are supported by 35 algorithms and 40 examples. Besides its practical usage, the given text with 36 figures and 11 tables, partially in colour, represents a valuable background for understanding, developing and applying various numerical methods, such as interpolation, numerical integration and solving partial differential equations, which are topics in the further volumes of the series Numerical Methods.
Download or read book Fundamentals of Approximation Theory written by Hrushikesh Narhar Mhaskar and published by CRC Press. This book was released on 2000 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Approximation of Functions Theory and Numerical Methods written by Günter Meinardus and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: for 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.
Download or read book Smoothing and Approximation of Functions written by Harold S. Shapiro and published by . This book was released on 1969 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation of Functions of Several Variables and Imbedding Theorems written by S.M. Nikol'skii and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: This English translation of my book "PribliZenie Funkcir Mnogih Peremennyh i Teoremy Vlozel1iya" is identical in content with the Rus sian original, published by "Nauka" in 1969. However, I have corrected a number of errors. I am grateful to the publishing house Springer-Verlag for making my book available to mathematicians who do not know Russian. I am also especially grateful to the translator, Professor John M. Dan skin, who has fulfilled his task with painstaking care. In doing so he has showed high qualifications both as a mathematician and as a translator of Russian, which is considered by many to be a very difficult language. The discussion in this book is restricted, for the most part, to func tions everywhere defined in n-dimensional space. The study of these questions for functions given on bounded regions requires new methods. In. connection with this I note that a new book, "Integral Represen tations of Functions and Imbedding Theorems", by O.V. Besov, V.P. Il'in, and myself, has just (May 1975) been published, by the publishing house "Nauka", in Moscow. Moscow, U.S.S.R., May 1975 S.M. Nikol'skir Translator's Note I am very grateful to Professor Nikol'skir, whose knowledge of English, which is considered by many to be a very difficult language, is excellent, for much help in achieving a correct translation of his book. And I join Professor Nikol'skir in thanking Springer-Verlag. The editing problem was considerable, and the typographical problem formidable