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Mathematics of Approximation [electronic resource] / by Johan Villiers.

By: Villiers, Johan [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Mathematics Textbooks for Science and Engineering: 1Publisher: Paris : Atlantis Press : Imprint: Atlantis Press, 2012Description: XXI, 406 p. 2 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9789491216503.Subject(s): Mathematics | Computer science | Computer science -- Mathematics | Engineering mathematics | Mathematics | Mathematics, general | Computational Mathematics and Numerical Analysis | Approximations and Expansions | Mathematics of Computing | Appl.Mathematics/Computational Methods of EngineeringDDC classification: 510 Online resources: Click here to access online
Contents:
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.
In: Springer eBooksSummary: 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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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.

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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