Abstract
This chapter is devoted to the approximation of a given real function by a simpler one that belongs, for example, to ℙ n , the set of polynomials of degree less than or equal to n. We also consider approximation by piecewise polynomial functions, that is, functions whose restrictions to some prescribed intervals are polynomials. The definitions and results of this chapter, given without proofs, are widely used in the rest of the book. We refer the reader to books on polynomial approximation theory, for instance (1989), (1993), and R(1981).
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Chapter References
G. Allaire and S.M. Kaber, Numerical Linear Algebra, Springer, New York, forthcoming, 2007.
C. Bernardi and Y. Maday, Spectral Methods, in Handbook of numerical analysis, Vol. V, North-Holland, Amsterdam, 1997.
A. Cohen, Numerical Analysis of Wavelet Methods, Studies in mathematics and its applications, North-Holland, Amsterdam, 2003.
M. Crouzeix and A. Mignot, Analyse numérique des équations différentielles, Masson, Paris, 1989.
R. A. De vore and G. G. Lorentz, Constructive Approximation, Springer-Verlag, Berlin, 1993.
T. J. Rivlin, An Introduction to the Approximation of Functions, Dover Publications Inc., New York, 1981.
L. Schwartz, Analyse, topologie générale et analyse fonctionnelle, Hrmann, Paris, 1980.
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(2007). Polynomial Approximation. In: Danaila, I., Joly, P., Kaber, S.M., Postel, M. (eds) An Introduction to Scientific Computing. Springer, New York, NY. https://doi.org/10.1007/978-0-387-49159-2_3
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DOI: https://doi.org/10.1007/978-0-387-49159-2_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-30889-0
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