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 computeraided 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 selfcontained. 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 NewtonCotes , Gauss and ClenshawCurtis quadrature the EulerMaclaurin 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
About Johan De Villiers
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Author  :  Johan De Villiers 
Publisher  :  Atlantis Press (Zeger Karssen) 
Data Published  :  01 July 2012 
ISBN  :  949121649X 
EAN  :  9789491216497 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  406 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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