Interpolation And Approximation By Polynomials

Author : George M. Phillips
Publisher : Springer Science & Business Media
Page : 325 pages
File Size : 40,8 Mb
Release : 2006-04-06
Category : Mathematics
ISBN : 9780387216829

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Interpolation and Approximation by Polynomials by George M. Phillips Pdf

In addition to coverage of univariate interpolation and approximation, the text includes material on multivariate interpolation and multivariate numerical integration, a generalization of the Bernstein polynomials that has not previously appeared in book form, and a greater coverage of Peano kernel theory than is found in most textbooks. There are many worked examples and each section ends with a number of carefully selected problems that extend the student's understanding of the text. The author is well known for his clarity of writing and his many contributions as a researcher in approximation theory.

Author : N. K. Govil,H. N. Mhaskar,Ram N. Mohapatra,Zuhair Nashed,J. Szabados
Publisher : CRC Press
Page : 476 pages
File Size : 55,6 Mb
Release : 2006-07-20
Category : Mathematics
ISBN : 9781420011388

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Frontiers in Interpolation and Approximation by N. K. Govil,H. N. Mhaskar,Ram N. Mohapatra,Zuhair Nashed,J. Szabados Pdf

Dedicated to the well-respected research mathematician Ambikeshwar Sharma, Frontiers in Interpolation and Approximation explores approximation theory, interpolation theory, and classical analysis. Written by authoritative international mathematicians, this book presents many important results in classical analysis, wavelets, and interpolation theory. Some topics covered are Markov inequalities for multivariate polynomials, analogues of Chebyshev and Bernstein inequalities for multivariate polynomials, various measures of the smoothness of functions, and the equivalence of Hausdorff continuity and pointwise Hausdorff-Lipschitz continuity of a restricted center multifunction. The book also provides basic facts about interpolation, discussing classes of entire functions such as algebraic polynomials, trigonometric polynomials, and nonperiodic transcendental entire functions. Containing both original research and comprehensive surveys, this book provides researchers and graduate students with important results of interpolation and approximation.

Author : Richard S. Varga
Publisher : Unknown
Page : 148 pages
File Size : 41,6 Mb
Release : 1982
Category : Approximation theory
ISBN : UVA:X001473303

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Topics in Polynomial and Rational Interpolation and Approximation by Richard S. Varga Pdf

Author : Philip J. Davis
Publisher : Courier Corporation
Page : 418 pages
File Size : 40,7 Mb
Release : 1975-01-01
Category : Mathematics
ISBN : 9780486624952

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Interpolation and Approximation by Philip J. Davis Pdf

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.

Author : J. L. Walsh
Publisher : American Mathematical Soc.
Page : 418 pages
File Size : 41,7 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 : 44,8 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 : Giorgio Celant,Michel Broniatowski
Publisher : John Wiley & Sons
Page : 254 pages
File Size : 43,8 Mb
Release : 2016-03-31
Category : Mathematics
ISBN : 9781119292289

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Interpolation and Extrapolation Optimal Designs V1 by Giorgio Celant,Michel Broniatowski Pdf

This book is the first of a series which focuses on the interpolation and extrapolation of optimal designs, an area with significant applications in engineering, physics, chemistry and most experimental fields. In this volume, the authors emphasize the importance of problems associated with the construction of design. After a brief introduction on how the theory of optimal designs meets the theory of the uniform approximation of functions, the authors introduce the basic elements to design planning and link the statistical theory of optimal design and the theory of the uniform approximation of functions. The appendices provide the reader with material to accompany the proofs discussed throughout the book.

Author : Theodore J. Rivlin
Publisher : Courier Corporation
Page : 164 pages
File Size : 51,8 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 : Ronald A. DeVore,George G. Lorentz
Publisher : Springer Science & Business Media
Page : 468 pages
File Size : 46,6 Mb
Release : 1993-11-04
Category : Mathematics
ISBN : 3540506276

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Constructive Approximation by Ronald A. DeVore,George G. Lorentz Pdf

Coupled with its sequel, this book gives a connected, unified exposition of Approximation Theory for functions of one real variable. It describes spaces of functions such as Sobolev, Lipschitz, Besov rearrangement-invariant function spaces and interpolation of operators. Other topics include Weierstrauss and best approximation theorems, properties of polynomials and splines. It contains history and proofs with an emphasis on principal results.

Author : Manfred Reimer
Publisher : Birkhäuser
Page : 361 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880954

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Multivariate Polynomial Approximation by Manfred Reimer Pdf

This book introduces general theory by presenting the most important facts on multivariate interpolation, quadrature, orthogonal projections and their summation, all treated under a constructive view, and embedded in the theory of positive linear operators. On this background, the book builds the first comprehensive introduction to the theory of generalized hyperinterpolation. Several parts of the book are based on rotation principles, which are presented in the beginning of the book.

Author : B.N. Sahney
Publisher : Springer
Page : 344 pages
File Size : 43,5 Mb
Release : 1979-05-31
Category : Mathematics
ISBN : UCAL:B5008706

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Polynomial and Spline Approximation by B.N. Sahney Pdf

Proceedings of the NATO Advanced Study Institute, Calgary, Canada, August 26-September 2, 1978

Author : R.D Harding,D.A Quinney
Publisher : CRC Press
Page : 190 pages
File Size : 49,6 Mb
Release : 1989-01-01
Category : Mathematics
ISBN : 0852741545

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A Simple Introduction to Numerical Analysis by R.D Harding,D.A Quinney Pdf

Approximation techniques are widely used in mathematics and applied physics, as exact solutions are frequently impossible to obtain. A Simple Introduction to Numerical Analysis, Volume 2: Interpolation and Approximation extends the first volume to consider problems in interpolation and approximation. Topics covered include the construction of interpolating functions, the determination of polynomial and rational function approximations, numerical quadrature, and the solution of boundary value problems in ordinary differential equations. As with the previous volume, the text is integrated with a software package that allows the reader to work through numerous examples. It is also possible to use the software to consider problems that are beyond the scope of the text. The authors' expertise in combining text and software has resulted in a very readable work.

Author : Lloyd N. Trefethen
Publisher : SIAM
Page : 295 pages
File Size : 41,5 Mb
Release : 2013-01-03
Category : Mathematics
ISBN : 161197240X

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Approximation Theory and Approximation Practice by Lloyd N. Trefethen Pdf

An original and modern treatment of approximation theory for students in applied mathematics. Includes exercises, illustrations and Matlab code.

Author : Boris I. Kvasov
Publisher : World Scientific
Page : 360 pages
File Size : 50,8 Mb
Release : 2000
Category : Mathematics
ISBN : 9810240104

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Methods of Shape-preserving Spline Approximation by Boris I. Kvasov Pdf

This book aims to develop algorithms of shape-preserving spline approximation for curves/surfaces with automatic choice of the tension parameters. The resulting curves/surfaces retain geometric properties of the initial data, such as positivity, monotonicity, convexity, linear and planar sections. The main tools used are generalized tension splines and B-splines. A difference method for constructing tension splines is also developed which permits one to avoid the computation of hyperbolic functions and provides other computational advantages. The algorithms of monotonizing parametrization described improve an adequate representation of the resulting shape-preserving curves/surfaces. Detailed descriptions of algorithms are given, with a strong emphasis on their computer implementation. These algorithms can be applied to solve many problems in computer-aided geometric design.

Author : Le Baron O. Ferguson
Publisher : American Mathematical Soc.
Page : 174 pages
File Size : 43,9 Mb
Release : 1980
Category : Mathematics
ISBN : 9780821815175

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Approximation by Polynomials with Integral Coefficients by Le Baron O. Ferguson Pdf

Addresses two questions that include: 'What functions can be approximated by polynomials whose coefficients are integers?' and 'How well are they approximated (Jackson type theorems)?'