Mathematics of Approximation
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…
Read More ↓Title Statements
- Full title :Mathematics of Approximation / by Johan Villiers.
Summary
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.
Read More ↓Edition Statements
- Publication Date:2012.
Publication Statements
- Publisher(s):Atlantis Press
- Place of Publication:Paris
- Language:eng
- Publication Date:2012.
Notes
Titre de l'écran-titre (visionné le 16 mai 2014).
NOTICE EN COURS DE TRAITEMENT.
The Physical Object
- Description:1 ressource en ligne
Edition Identifiers
- ISBN:9789491216503, 9491216503
- oclc:ocn880937088
- LC Classification:QA1-939
- Dewey Decimal:510
Table of Contents
<P>Polynomial Interpolation Formulas -- Error Analysis For Polynomial Interpolation -- Polynomial Uniform Convergence -- Best Approximation -- Approximation Operators -- Best Uniform Polynomial Approximation -- Orthogonality -- Interpolatory Quadrature -- Approximation of Periodic Functions -- Spline Approximation.</p>.
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