## Approximation Theory And Methods

**Author**: M. J. D. Powell

**Publisher:**Cambridge University Press

**ISBN:**9780521295147

**File Size**: 61,13 MB

**Format:**PDF, ePub, Mobi

**Read:**4795

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.

## Approximation Theory And Methods

**Author**: M. J. D. Powell

**Publisher:**Cambridge University Press

**ISBN:**9780521224727

**File Size**: 36,21 MB

**Format:**PDF

**Read:**439

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.

## Approximation Theory And Methods

**Author**: M. J. D. Powell

**Publisher:**Cambridge University Press

**ISBN:**9780521295147

**File Size**: 25,35 MB

**Format:**PDF, ePub, Mobi

**Read:**8823

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.

## Approximation Theory And Numerical Methods

**Author**: G. A. Watson

**Publisher:**John Wiley & Sons

**ISBN:**

**File Size**: 60,89 MB

**Format:**PDF, Docs

**Read:**1216

## Approximation Theory And Approximation Practice

**Author**: Lloyd N. Trefethen

**Publisher:**SIAM

**ISBN:**9781611972405

**File Size**: 44,27 MB

**Format:**PDF, ePub

**Read:**5541

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

## Methods Of Approximation Theory

**Author**: Alexander I. Stepanets

**Publisher:**Walter de Gruyter

**ISBN:**3110195283

**File Size**: 73,17 MB

**Format:**PDF, Mobi

**Read:**2840

## Methods Of Approximation Theory In Complex Analysis And Mathematical Physics

**Author**: Andrei A. Gonchar

**Publisher:**Springer

**ISBN:**3540477926

**File Size**: 25,39 MB

**Format:**PDF, ePub, Docs

**Read:**6723

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.

## An Introduction To The Approximation Of Functions

**Author**: Theodore J. Rivlin

**Publisher:**Courier Corporation

**ISBN:**9780486640693

**File Size**: 79,29 MB

**Format:**PDF, ePub, Mobi

**Read:**271

Mathematics of Computing -- Numerical Analysis.

## Approximation Theory And Optimization

**Author**: Michael James David Powell

**Publisher:**Cambridge University Press

**ISBN:**9780521581905

**File Size**: 33,90 MB

**Format:**PDF, ePub, Docs

**Read:**6245

Authorities in numerical analysis and optimisation combine to write an important volume in the area.

## Model Reduction And Approximation

**Author**: Peter Benner

**Publisher:**SIAM

**ISBN:**1611974828

**File Size**: 20,33 MB

**Format:**PDF, ePub, Docs

**Read:**2766

Many physical, chemical, biomedical, and technical processes can be described by partial differential equations or dynamical systems. In spite of increasing computational capacities, many problems are of such high complexity that they are solvable only with severe simplifications, and the design of efficient numerical schemes remains a central research challenge. This book presents a tutorial introduction to recent developments in mathematical methods for model reduction and approximation of complex systems. Model Reduction and Approximation: Theory and Algorithms contains three parts that cover (I) sampling-based methods, such as the reduced basis method and proper orthogonal decomposition, (II) approximation of high-dimensional problems by low-rank tensor techniques, and (III) system-theoretic methods, such as balanced truncation, interpolatory methods, and the Loewner framework. It is tutorial in nature, giving an accessible introduction to state-of-the-art model reduction and approximation methods. It also covers a wide range of methods drawn from typically distinct communities (sampling based, tensor based, system-theoretic).?? This book is intended for researchers interested in model reduction and approximation, particularly graduate students and young researchers.