Cardinal interpolation and spline functions VIII. The budan-fourier theorem for splines and applications

  • Carl de Boor
  • I. J. Schoenberg
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 501)


Sign Structure Simple Zero Power Growth Spline Interpolant Cardinal Spline 
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  1. 1.
    G. Birkhoff and C. de Boor, Error bounds for spline interpolation, J. Math. Mech. 13 (1964) 827–836.MathSciNetzbMATHGoogle Scholar
  2. 2.
    C. de Boor, On cubic spline functions which vanish at all knots, MRC TSR 1424, 1974; Adv. Math. (1975).Google Scholar
  3. 3.
    H. G. Burchard, Extremal positive splines with applications to interpolation and approximation by generalized convex functions, Bull. Amer. Math. Soc. 79 (1973) 959–963.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    A. Cavaretta, Jr., An elementary proof of Kolmogorov's theorem, Amer. Math. Monthly, 81 (1974), 480–486.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    F. R. Gantmacher and M. G. Krein, “Oszillationsmatrizen, Oszillationskerne und kleine Schwingungen mechanischer Systeme”, (transl. from 2nd Russian ed. of 1950), Akademie Verlag, Berlin, 1960.Google Scholar
  6. 6.
    Charles A. Hall and W. Weston Meyer, Optimal error bounds for cubic spline interpolation, GMR-1556, Gen. Motors Res. Labs., Warren, Michigan, Mar. 1974, iii+25pp.Google Scholar
  7. 7.
    S. Karlin and C. Micchelli, The fundamental theorem of algebra for monosplines satisfying boundary conditions, Israel J. Math. 11 (1972) 405–451.MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    А. Н. Колмогоров, О Неравенствах межлу верхними гранями посделоватедгнщх производнщх функции на Бесионечном интерваде, Ччен. зап. МГУ, ВЫР. 30, “Математука”, 30 (1939), 3–13; a translation into English has appeared as: A. N. Kolmogorov, On inequalities between upper bounds of the successive derivatives of an arbitrary function on an infinite interval, in Amer. Mathem. Soc. Translations 4 (1949) 233–243.Google Scholar
  9. 9.
    E. Landau, Einige Ungleichungen für zweimal differentiirbare Funktionen, Proc. London Math. Soc. (2) 13 (1913) 43–49.zbMATHGoogle Scholar
  10. 10.
    C. A. Micchelli, Cardinal £-splines, in “Studies in splines and approximation theory”, S. Karlin, C. A. Micchelli, A. Pinkus and I. J. Schoenberg, Academic Press, New York, 1975.Google Scholar
  11. 11.
    C. A. Micchelli, Oscillation matrices and cardinal spline interpolation, in “Studies in splines and approximation theory”, S. Karlin et al., Academic Press, New York, 1975.Google Scholar
  12. 12.
    E. N. Nilson, Polynomial splines and a fundamental eigenvalue problem for polynomials, J. Approx. Theory 6 (1972) 439–465.MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    F. Richards, Best bounds for the uniform periodic spline interpolation operator, J. Approx. Theory 7 (1973) 302–317.MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    I. J. Schoenberg, Zur Abzählung der reellen Wurzeln algebraischer Gleichungen, Math. Zeit. 38 (1934) 546–564.MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    I. J. Schoenberg, “Cardinal Spline Interpolation”, CBMS Vol. 12, SIAM, Philadelphia, 1973.CrossRefzbMATHGoogle Scholar
  16. 16.
    I. J. Schoenberg, The elementary cases of Landau's problem of inequalities between derivatives, Amer. Math. Monthly 80 (1973) 121–148.MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    I. J. Schoenberg, On remainders and the convergence of cardinal spline interpolation for almost periodic functions, MRC TSR 1514, Dec. 1974; in “Studies in splines and approximation theory”, S. Karlin et al., Academic Press, New York, 1975.Google Scholar
  18. 18.
    I. J. Schoenberg, On Charles Micchelli's theory of cardinal £-splines, MRC TSR 1511, Dec. 1974; in “Studies in splines and approximation theory”, S. Karlin et al., Academic Press, New York, 1975.Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Carl de Boor
  • I. J. Schoenberg

There are no affiliations available

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