Advertisement

Abstract

Consider a family of functions of a single variable x,
$$\Phi (x;{a_0},...,{a_n}),$$
having n + 1 parameters a 0, ... , a n , whose values characterize the individual functions in this family.

Keywords

Rational Expression Spline Function Polynomial Interpolation Interpolation Problem Support Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References for Chapter 2

  1. Achieser, N. I.: Theory of Approximations. Translated from the Russian by C. Hyman. New York: Frederick Ungar 1956.Google Scholar
  2. Ahlberg, J., Nilson, E., Walsh, J.: The Theory of Splines and Their Applications. New York: Academic Press 1967.MATHGoogle Scholar
  3. Bloomfield, P.: Fourier Analysis of Time Series. New York: Wiley 1976.MATHGoogle Scholar
  4. Böhmer, K.: Spline-Funktionen. Stuttgart: Teubner 1974.Google Scholar
  5. Brigham, E. O.: The Fast Fourier Transform. Englewood Cliffs, N.J.: Prentice-Hall 1974.Google Scholar
  6. Bulirsch, R., Rutishauser, H.: Interpolation und genäherte Quadratur. In: Sauer, Szabó (1968).Google Scholar
  7. Bulirsch, R., Stoer, J.: Darstellung von Funktionen in Rechenautomaten. In: Sauer, Szabó (1968).Google Scholar
  8. Ciarlet, P. G., Schultz, M. H., Varga, R. S.: Numerical methods of high-order accuracy for nonlinear boundary value problems I. One dimensional problems. Numer. Math. 9, 394–430 (1967).MathSciNetMATHCrossRefGoogle Scholar
  9. Cooley, J. W., Tukey, J. W.: An algorithm for the machine calculation of complex Fourier series. Math. Comput. 19, 297–301 (1965).MathSciNetMATHCrossRefGoogle Scholar
  10. Davis, P. J.: Interpolation and Approximation. New York: Blaisdell 1963, 2nd printing 1965.Google Scholar
  11. de Boor, G.: On calculating with B-splines. J. Approximation Theory 6, 50–62 (1972).MathSciNetMATHCrossRefGoogle Scholar
  12. de Boor, G.: A Practical Guide to Splines. New York: Springer-Verlag 1978.MATHCrossRefGoogle Scholar
  13. Gautschi, W.: Attenuation factors in practical Fourier analysis. Numer. Math. 18, 373–400 (1972).MathSciNetMATHCrossRefGoogle Scholar
  14. Gentleman, W. M., Sande, G.: Fast Fourier transforms—for fun and profit. In: Proc. AFIPS 1966 Fall Joint Computer Conference, 29, 503–578. Washington D.C.: Spartan Books 1966.Google Scholar
  15. Goertzel, G.: An algorithm for the evaluation of finite trigonometric series. Amer. Math. Monthly 65, 34–35 (1958).MathSciNetMATHCrossRefGoogle Scholar
  16. Greville, T. N. E.: Introduction to spline functions. In: Theory and Applications of Spline Functions. Edited by T. N. E. Greville. New York: Academic Press 1969.Google Scholar
  17. Hall, C. A., Meyer, W. W.: Optimal error bounds for cubic spline interpolation. J. Approx. Theory 16, 105–122 (1976).MathSciNetMATHCrossRefGoogle Scholar
  18. Herriot, J. G., Reinsch, C.: algol 60 Procedures for the calculation of interpolating natural spline functions. Technical Report STAN-CS-71–200, Computer Science Department, Stanford University, California 1971.MATHGoogle Scholar
  19. Kuntzmann, J.: Méthodes Numériques, InterpolationDérivées. Paris: Dunod 1959.MATHGoogle Scholar
  20. Maehly, H., Witzgall, Ch.: Tschebyscheff-Approximationen in kleinen Intervallen II. Numer. Math. 2, 293–307 (1960).MathSciNetCrossRefGoogle Scholar
  21. Milne, E. W.: Numerical Calculus. Princeton, N.J.: Princeton University Press 1949, 2nd printing 1950.Google Scholar
  22. Milne-Thomson, L. M.: The Calculus of Finite Differences. London: Macmillan 1933, reprinted 1951.Google Scholar
  23. Reinsch, C.: Unpublished manuscript.Google Scholar
  24. Sauer, R., Szabó, I. (editors): Mathematische Hilfsmittel des Ingenieurs, Part III. Berlin, Heidelberg, New York: Springer 1968.Google Scholar
  25. Schultz, M. H.: Spline Analysis. Englewood Cliffs, N.J.: Prentice-Hall 1973.MATHGoogle Scholar
  26. Singleton, R. C.: On computing the fast Fourier transform. Comm. ACM 10, 647–654 (1967).MathSciNetMATHCrossRefGoogle Scholar
  27. Singleton, R. C.: Algorithm 338: algol procedures for the fast Fourier transform. Algorithm 339: an algol Procedure for the fast Fourier transform with arbitrary factors. Comm. ACM. 11, 773–779 (1968).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1980

Authors and Affiliations

  • J. Stoer
    • 1
  • R. Bulirsch
    • 2
  1. 1.Institut für Angewandte MathematikUniversität Würzburg am HublandWürzburgFederal Republic of Germany
  2. 2.Institut für MathematikTechnische UniversitätMünchenFederal Republic of Germany

Personalised recommendations