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
G. Birkhoff and C. de Boor, Error bounds for spline interpolation, J. Math. Mech. 13 (1964) 827–836.
C. de Boor, On cubic spline functions which vanish at all knots, MRC TSR 1424, 1974; Adv. Math. (1975).
H. G. Burchard, Extremal positive splines with applications to interpolation and approximation by generalized convex functions, Bull. Amer. Math. Soc. 79 (1973) 959–963.
A. Cavaretta, Jr., An elementary proof of Kolmogorov's theorem, Amer. Math. Monthly, 81 (1974), 480–486.
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.
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.
S. Karlin and C. Micchelli, The fundamental theorem of algebra for monosplines satisfying boundary conditions, Israel J. Math. 11 (1972) 405–451.
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.
E. Landau, Einige Ungleichungen für zweimal differentiirbare Funktionen, Proc. London Math. Soc. (2) 13 (1913) 43–49.
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.
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.
E. N. Nilson, Polynomial splines and a fundamental eigenvalue problem for polynomials, J. Approx. Theory 6 (1972) 439–465.
F. Richards, Best bounds for the uniform periodic spline interpolation operator, J. Approx. Theory 7 (1973) 302–317.
I. J. Schoenberg, Zur Abzählung der reellen Wurzeln algebraischer Gleichungen, Math. Zeit. 38 (1934) 546–564.
I. J. Schoenberg, “Cardinal Spline Interpolation”, CBMS Vol. 12, SIAM, Philadelphia, 1973.
I. J. Schoenberg, The elementary cases of Landau's problem of inequalities between derivatives, Amer. Math. Monthly 80 (1973) 121–148.
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.
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.
Editor information
Additional information
Dedicated to M. G. Krein
Rights and permissions
Copyright information
© 1976 Springer-Verlag
About this paper
Cite this paper
de Boor, C., Schoenberg, I.J. (1976). Cardinal interpolation and spline functions VIII. The budan-fourier theorem for splines and applications. In: Böhmer, K., Meinardus, G., Schempp, W. (eds) Spline Functions. Lecture Notes in Mathematics, vol 501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079740
Download citation
DOI: https://doi.org/10.1007/BFb0079740
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-07543-1
Online ISBN: 978-3-540-38073-3
eBook Packages: Springer Book Archive