Abstract
This paper is concerned with Budan-Fourier theorems for rather general classes of spline functions. We extend the results known up to now, and at the same time simplify the underlying analysis. Some special cases are added.
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Literatur
BIRKHOFF, G.D., General mean value and remainder theorems with applications to mechanical differentiation and quadrature. Trans. Amer.Math.Soc. 7 (1906), 107–136.
deBOOR, C. and I.J. SCHOENBERG, Cardinal interpolation and spline functions VIII. The Budan-Fourier theorem for splines and applications. In "Spline Functions", K. Böhmer, G. Meinardus and W. Schempp, Eds. Berlin-Heidelberg-New York: Springer-Verlag 1976, 1–79.
FERGUSON, D.R., Sign changes and minimal support properties of Hermite-Birkhoff splines with compact support. SIAM J. Numer. Anal. 11 (1974), 769–779.
GANTMACHER, F.R. und M.G. KREIN, "Oszillationsmatrizen, Oszillationskerne und kleine Schwingungen mechanischer Systeme", Berlin: Akademie-Verlag 1960.
HOUSEHOLDER, M., "The numerical treatment of a single non-linear equation". New York: McGraw Hill, 1970.
JETTER,K., Duale Hermite-Birkhoff-Probleme. Erscheint in J. Approximation Theory.
JETTER,K., Birkhoff interpolation by splines. Erscheint im Tagungsband des Symposiums über Approximationstheorie, Austin 1976.
JOHNSON, R.C., On monosplines of least deviation. Trans.Amer.Math.Soc. 96 (1960), 458–477.
KARLIN, S. and L.L. SCHUMAKER, The fundamental theorem of algebra for Tchebycheffian monosplines. J. d'Anal.Math. 20 (1967), 233–270.
LORENTZ, G.G., Zeros of splines and Birkhoff's kernel. Math.Z. 142 (1975), 173–180.
LORENTZ, G.G. and K.L. ZELLER, Birkhoff interpolation. SIAM J.Numer.Anal. 8 (1971), 43–48.
MELKMAN, A.A., The Budan-Fourier theorem for splines. Israel J. Math. 19 (1974), 256–263.
MICCHELLI, C., The fundamental theorem of algebra for monosplines with multiplicities. Proc.Conf.Oberwolfach 1971, ISNM 20 (1972), 419–430.
SCHUMAKER,L.L., Zeros of spline functions and applications. Erscheint im J.Approximation Theory.
SCHUMAKER, L.L., Toward a constructive theory of generalized spline functions. In "Spline Functions", K. Böhmer, G. Meinardus and W. Schempp, Eds., Berlin-Heidelberg-New York: Springer-Verlag 1976, 265–331.
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Jetter, K. (1976). Nullstellen von Splines. In: Schaback, R., Scherer, K. (eds) Approximation Theory. Lecture Notes in Mathematics, vol 556. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0087413
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DOI: https://doi.org/10.1007/BFb0087413
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