Mathematical Functions And Their Approximations

Author : Yudell L. Luke
Publisher : Academic Press
Page : 586 pages
File Size : 43,5 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483262451

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Mathematical Functions and Their Approximations by Yudell L. Luke Pdf

Mathematical Functions and their Approximations is an updated version of the Applied Mathematics Series 55 Handbook based on the 1954 Conference on Mathematical Tables, held at Cambridge, Massachusetts. The aim of the conference is to determine the need for mathematical tables in view of the availability of high speed computing machinery. This work is composed of 14 chapters that cover the machinery for the expansion of the generalized hypergeometric function and other functions in infinite series of Jacobi and Chebyshev polynomials of the first kind. Numerical coefficients for Chebyshev expansions of the more common functions are tabulated. Other chapters contain polynomial and rational approximations for certain class of G-functions, the coefficients in the early polynomials of these rational approximations, and the Padé approximations for many of the elementary functions and the incomplete gamma functions. The remaining chapters describe the development of analytic approximations and expansions. This book will prove useful to mathematicians, advance mathematics students, and researchers.

Author : Yudell L. Luke
Publisher : Academic Press
Page : 348 pages
File Size : 44,8 Mb
Release : 1969
Category : Mathematics
ISBN : 9780080955605

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The Special Functions and Their Approximations by Yudell L. Luke Pdf

A detailed and self-contained and unified treatment of many mathematical functions which arise in applied problems, as well as the attendant mathematical theory for their approximations. many common features of the Bessel functions, Legendre functions, incomplete gamma functions, confluent hypergeometric functions, as well as of otherw, can be derived. Hitherto, many of the material upon which the volumes are based has been available only in papers scattered throughout the literature.

Author : Yudell L. Luke
Publisher : Academic Press
Page : 484 pages
File Size : 53,8 Mb
Release : 1969
Category : Computers
ISBN : 9780080955612

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Special Functions and Their Approximations: by Yudell L. Luke Pdf

Special Functions and Their Approximations: v. 2

Author : Theodore J. Rivlin
Publisher : Courier Corporation
Page : 164 pages
File Size : 41,8 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 : Milton Abramowitz,Irene A. Stegun
Publisher : Courier Corporation
Page : 1068 pages
File Size : 54,7 Mb
Release : 1965-01-01
Category : Mathematics
ISBN : 0486612724

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Handbook of Mathematical Functions by Milton Abramowitz,Irene A. Stegun Pdf

An extensive summary of mathematical functions that occur in physical and engineering problems

Author : Günter Meinardus
Publisher : Springer Science & Business Media
Page : 207 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642856433

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Approximation of Functions: Theory and Numerical Methods by Günter Meinardus Pdf

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.

Author : A. F. Timan
Publisher : Elsevier
Page : 644 pages
File Size : 46,5 Mb
Release : 2014-07-22
Category : Mathematics
ISBN : 9781483184814

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Theory of Approximation of Functions of a Real Variable by A. F. Timan Pdf

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.

Author : Johan De Villiers
Publisher : Springer Science & Business Media
Page : 406 pages
File Size : 46,5 Mb
Release : 2012-06-30
Category : Mathematics
ISBN : 9789491216503

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Mathematics of Approximation by Johan De Villiers Pdf

The approximation of a continuous function by either an algebraic polynomial, a trigonometric polynomial, or a spline, is an important issue in application areas like computer-aided geometric design and signal analysis. This book is an introduction to the mathematical analysis of such approximation, and, with the prerequisites of only calculus and linear algebra, the material is targeted at senior undergraduate level, with a treatment that is both rigorous and self-contained. The topics include polynomial interpolation; Bernstein polynomials and the Weierstrass theorem; best approximations in the general setting of normed linear spaces and inner product spaces; best uniform polynomial approximation; orthogonal polynomials; Newton-Cotes , Gauss and Clenshaw-Curtis quadrature; the Euler-Maclaurin formula ; approximation of periodic functions; the uniform convergence of Fourier series; spline approximation,with an extensive treatment of local spline interpolation,and its application in quadrature. Exercises are provided at the end of each chapter

Author : Gradimir V. Milovanović,Michael Th. Rassias
Publisher : Springer
Page : 880 pages
File Size : 43,7 Mb
Release : 2014-07-08
Category : Mathematics
ISBN : 9781493902583

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Analytic Number Theory, Approximation Theory, and Special Functions by Gradimir V. Milovanović,Michael Th. Rassias Pdf

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.

Author : J. L. Walsh
Publisher : American Mathematical Soc.
Page : 405 pages
File Size : 53,9 Mb
Release : 1935-12-31
Category : Mathematics
ISBN : 9780821810200

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Interpolation and Approximation by Rational Functions in the Complex Domain by J. L. Walsh Pdf

The present work is restricted to the representation of functions in the complex domain, particularly analytic functions, by sequences of polynomials or of more general rational functions whose poles are preassigned, the sequences being defined either by interpolation or by extremal properties (i.e. best approximation). Taylor's series plays a central role in this entire study, for it has properties of both interpolation and best approximation, and serves as a guide throughout the whole treatise. Indeed, almost every result given on the representation of functions is concerned with a generalization either of Taylor's series or of some property of Taylor's series--the title ``Generalizations of Taylor's Series'' would be appropriate.

Author : M. J. D. Powell
Publisher : Cambridge University Press
Page : 356 pages
File Size : 41,7 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 : Andrei A. Gonchar,Edward B. Saff
Publisher : Springer
Page : 225 pages
File Size : 45,5 Mb
Release : 2008-01-03
Category : Mathematics
ISBN : 9783540477921

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Methods of Approximation Theory in Complex Analysis and Mathematical Physics by Andrei A. Gonchar,Edward B. Saff Pdf

The book incorporates research papers and surveys written by participants ofan International Scientific Programme on Approximation Theory jointly supervised by Institute for Constructive Mathematics of University of South Florida at Tampa, USA and the Euler International Mathematical Instituteat St. Petersburg, Russia. The aim of the Programme was to present new developments in Constructive Approximation Theory. The topics of the papers are: asymptotic behaviour of orthogonal polynomials, rational approximation of classical functions, quadrature formulas, theory of n-widths, nonlinear approximation in Hardy algebras,numerical results on best polynomial approximations, wavelet analysis. FROM THE CONTENTS: E.A. Rakhmanov: Strong asymptotics for orthogonal polynomials associated with exponential weights on R.- A.L. Levin, E.B. Saff: Exact Convergence Rates for Best Lp Rational Approximation to the Signum Function and for Optimal Quadrature in Hp.- H. Stahl: Uniform Rational Approximation of x .- M. Rahman, S.K. Suslov: Classical Biorthogonal Rational Functions.- V.P. Havin, A. Presa Sague: Approximation properties of harmonic vector fields and differential forms.- O.G. Parfenov: Extremal problems for Blaschke products and N-widths.- A.J. Carpenter, R.S. Varga: Some Numerical Results on Best Uniform Polynomial Approximation of x on 0,1 .- J.S. Geronimo: Polynomials Orthogonal on the Unit Circle with Random Recurrence Coefficients.- S. Khrushchev: Parameters of orthogonal polynomials.- V.N. Temlyakov: The universality of the Fibonacci cubature formulas.

Author : Jean-Michel Muller
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 52,8 Mb
Release : 2006-09-11
Category : Computers
ISBN : 9780817644086

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Elementary Functions by Jean-Michel Muller Pdf

Second Edition of successful, well-reviewed Birkhauser book, which sold 866 copies in North America Provides an up-to-date presentation by including new results, examples, and problems throughout the text The second edition adds a chapter on multiple-precision arithmetic, and new algorithms invented since 1997

Author : Anonim
Publisher : American Mathematical Soc.
Page : 276 pages
File Size : 40,9 Mb
Release : 1965-12-31
Category : Approximation theory
ISBN : 0821896229

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Twelve Papers on Approximations and Integrals by Anonim Pdf

Author : S. B. Stechkin
Publisher : American Mathematical Soc.
Page : 144 pages
File Size : 44,9 Mb
Release : 1974
Category : Mathematics
ISBN : 0821830090

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Approximation of Periodic Functions by S. B. Stechkin Pdf

Papers and articles about periodic functions approximation.