Abstract
While interpolation attempts to approximate a functionpiecewise by polynomials which pass exactly through prescribed support points, we shall now try to approximate a given function f(x) on a (relatively large) intervalI by one polynomial. Such an approximation polynomial, naturally, must be of a higher degree than in the case where f(x) is approximated by polynomial pieces.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Achieser, N.I . [1956]: Theory of Approximation (Translated from the Russian by C.J. Hyman), Frederick Ungar Publ. Co., New York.
Brigham, E.O. [1974]: The Fast Fourier Transform, Prentice-Hall, Englewood Cliffs, N.J.
Clenshaw, C.W. [1962]: Chebyshev Series for Mathematical Functions, National Physical Laboratory Mathematical Tables 5, Her Majesty’s Stationery Office, London.
Clenshaw, C.W. and Picken, S.M. [1966]: Chebyshev Series for Bessel Functions of Fractional Order, National Physical Laboratory Mathematical Tables 8, Her Majesty’s Stationery Office, London.
Fox, L. and Parker, I.B. [1968]: Chebyshev Polynomials in Numerical Analysis, Oxford University Press, London.
Gautschi, W. [1975]: Computational methods in special functions - a survey, in Theory and Application of Special Functions (R.A. Askey, ed.), pp. 1–98, Academic Press, New York.
Gautschi, W. [1984]: Questions of numerical condition related to polynomials, in Studies in Numerical Analysis (G.H. Golub, ed.), pp. 140–177. Studies in Mathematics 24, The Mathematical Association of America.
Hart, J.F., Cheney, E.W., Lawson, C.L., Maehly, H.J., Mesztenyi, C.K., Rice, J.R., Thacher, H.C., Jr. and Witzgall, C. [1968]: Computer Approximations, Wiley, New York.
Henrici, P. [1979]: Fast Fourier methods in computational complex analysis, SIAM Rev. 21, 481–527.
Luke, Y.L. [1969]: The Special Functions and Their Approximations, Vols. I, II, Academic Press, New York.
National Bureau of Standards [1952]: Tables of Chebyshev Polynomials Sn(x) and Cn(x), Appl. Math. Ser. 9, U.S. Government Printing Office, Washington, D.C.
Nussbaumer, H.J. [1981]: Fast Fourier Transform and Convolution Algorithms, Springer, Berlin.
Paszkowski, S. [1975]: Numerical Applications of Chebyshev Polynomials and Series (Polish), Panstwowe Wydawnictwo Naukowe, Warsaw. [Russian translation in: “Nauka”, Fiz.-Mat. Lit., Moscow, 1983].
Ralston, A. [1967]: Rational Chebyshev approximation, in Mathematical Methods for Digital Computers, Vol. 2 (A. Ralston and H.S. Wilf, eds.), pp. 264–284. Wiley, New York.
Rivlin, T.J. [1974]: The Chebyshev Polynomials, Wiley, New York.
Temperton, C. [1983]: Self-sorting mixed-radix fast Fourier transforms, J. Comput. Phys. 52, 1–23.
Editor information
Rights and permissions
Copyright information
© 1990 Birkhäuser Boston
About this chapter
Cite this chapter
Rutishauser, H. (1990). Approximation. In: Gutknecht, M. (eds) Lectures on Numerical Mathematics. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3468-5_7
Download citation
DOI: https://doi.org/10.1007/978-1-4612-3468-5_7
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-8035-4
Online ISBN: 978-1-4612-3468-5
eBook Packages: Springer Book Archive