Mathematics of Approximation (Mathematics Textbooks for Science and Engineering, 1, Band 1) - Hardcover

De Villiers, Johan

Hardcover

ISBN 10: 949121649X ISBN 13: 9789491216497

Verlag: Atlantis Press, 2012

Inhaltsangabe

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

Details zur Ausgabe

• Verlag: Atlantis Press
• Erscheinungsdatum: 2012
• Sprache: Englisch
• ISBN 10: 949121649X
• ISBN 13: 9789491216497
• Einband: Gebundene Ausgabe
• Anzahl der Seiten: 427
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