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130626 ||| eng |
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|a 9789491216503
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| 100 |
1 |
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|a De Villiers, Johan
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| 245 |
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|a Mathematics of Approximation
|h Elektronische Ressource
|c by Johan De Villiers
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| 250 |
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|a 1st ed. 2012
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| 260 |
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|a Paris
|b Atlantis Press
|c 2012, 2012
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| 300 |
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|a XXI, 406 p
|b online resource
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| 505 |
0 |
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|a 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
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| 653 |
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|a Mathematics of Computing
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| 653 |
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|a Engineering mathematics
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| 653 |
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|a Computer science / Mathematics
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| 653 |
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|a Computational Mathematics and Numerical Analysis
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| 653 |
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|a Approximations and Expansions
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| 653 |
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|a Mathematics / Data processing
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| 653 |
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|a Engineering / Data processing
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| 653 |
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|a Mathematics
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| 653 |
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|a Approximation theory
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| 653 |
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|a Mathematical and Computational Engineering Applications
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| 041 |
0 |
7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b Springer
|a Springer eBooks 2005-
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| 490 |
0 |
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|a Mathematics Textbooks for Science and Engineering
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| 028 |
5 |
0 |
|a 10.2991/978-94-91216-50-3
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| 856 |
4 |
0 |
|u https://doi.org/10.2991/978-94-91216-50-3?nosfx=y
|x Verlag
|3 Volltext
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| 082 |
0 |
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|a 510
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| 520 |
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|a 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
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