approximation theory and methods

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Approximation Theory And Methods

Author : M. J. D. Powell
ISBN : 0521295149
Genre : Mathematics
File Size : 35. 2 MB
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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.

Methods Of Approximation Theory

Author : Alexander I. Stepanets
ISBN : 9783110195286
Genre : Mathematics
File Size : 90. 91 MB
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Approximation Theory And Numerical Methods

Author : G. A. Watson
ISBN : UOM:39015015733853
Genre : Mathematics
File Size : 38. 58 MB
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Methods Of Functional Analysis In Approximation Theory

Author : Charles A. Micchelli
ISBN : 3764317612
Genre : Mathematics
File Size : 66. 9 MB
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Approximation Theory And Optimization

Author : M. D. Buhmann
ISBN : 0521581907
Genre : Mathematics
File Size : 26. 20 MB
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Authorities in numerical analysis and optimisation combine to write an important volume in the area.

Methods Of Approximation Theory In Complex Analysis And Mathematical Physics

Author : Andrei A. Gonchar
ISBN : 9783540477921
Genre : Mathematics
File Size : 46. 35 MB
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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.

Functional Analysis And Approximation Theory In Numerical Analysis

Author : R. S. Varga
ISBN : 9780898710038
Genre : Mathematics
File Size : 64. 35 MB
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Surveys the enormous literature on numerical approximation of solutions of elliptic boundary problems by means of variational and finite element methods, requiring almost constant application of results and techniques from functional analysis and approximation theory to the field of numerical analysis.

Approximation Theory And Approximation Practice

Author : Lloyd N. Trefethen
ISBN : 161197240X
Genre : Mathematics
File Size : 72. 34 MB
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An original and modern treatment of approximation theory for students in applied mathematics. Includes exercises, illustrations and Matlab code.

Complex Methods In Approximation Theory

Author : Francisco Marcellán
ISBN : 8482400460
Genre : Mathematics
File Size : 81. 25 MB
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This book provides an up-to-date account of research in Approximation Theory and Complex Analysis, areas which are the subject of recent exciting developments.The level of presentation should be suitable for anyone with a good knowledge of analysis, including scientists with a mathematical background. The volume contains both research papers and surveys, presented by specialists in the field. The areas discussed are: Orthogonal Polynomials (with respect to classical and Sobolev inner products), Approximation in Several Complex Variables, Korovkin-type Theorems, Potential Theory, Ratinal Approximation and Linear Ordinary Differential Equations.

Numerical Methods In Approximation Theory

Author : D. Braess
ISBN : 9783034886192
Genre : Juvenile Nonfiction
File Size : 37. 55 MB
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This book is the official proceedings of a conference on Numerical Methods in Approximation Theory which was held at the Mathematisches Forschungs institut in Oberwolfach during the week of November 24~30, 1991. It contains refereed and edited papers by 20 of the 49 participants. The book is dedicated to the memory of Prof. Lothar Collatz who main tained a long and active interest in numerical approximation. It is the ninth in a series of volumes published by Birkhiiuser resulting from conferences on the subject held at Oberwolfach, and co-organized by Prof. Collatz. We now briefly describe the contents of the book. The paper of BASZEN SKI, DELVOS and JESTER deals with blending using sine double series expan sions of functions defined on the unit square. In addition to giving explicit error estimates for partial sums and for interpolating sine polynomials, they also show that Boolean sums yield almost the same asymptotic error estimates as the conventional tensor-product approach, but with a reduced number of terms. The paper of BEATSON and LIGHT discusses approximation by quasi interpolants which are sums of scaled translates of a one-parameter family of functions. They do not require reproduction of low degree polynomials, but nevertheless are able to give error bounds and analyze quasi-interpolation based on Gaussians and exponentials. BINEV and JETTER deal with multivariate interpolation using shifts of a single basis function. They treat both gridded data and scattered data. As examples, they consider box splines and certain radial basis functions.

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