Abstract
In the previous chapter, you learned something about splines and their properties. Now you know some types of splines (interpolating, smoothing, and mixed), some criteria of existence and uniqueness of such splines, some examples of spline-functions.
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Bibliography
Atteia, M. (1970) : “Fonctions ’spline’ et noyaux reproduisants d’Aronszajn-Bergman”, R. I. R. O., R-3, pp. 31–43
Aronszajn, N. (1950): “Theory of reproducing kernals” ,(Trans. Amer. Math. Soc.) Vol. 68, No. 1–3, pp. 337–407
Bezhaev, A.Yu. (1990): “Reproducing mappings and vector splinefunctions” , in Sov. J. Numer. Math. Modelling, Vol. 5, No. 2, pp. 91–110 (VNU Science Press, Utrecht)
Bezhaev A.Yu. (1991): “Reproducing mappings of Hilbert spaces and characterization of operator splines” , in Modelirovanie v Mekhanike, Novosibirsk Computing Center, Inst. Theoret. Applied Mechanics. Vol. 5(22), No. 1, pp. 3–16 [in Russian]
Duchon, J. (1977): “Splines minimizing rotation-invariant seminorms in Sobolev spaces” , in Lect. Notes in Math. Vol. 571, pp. 85–100
Freeden, W. (1980): “On integral formulas of the (Unit) Sphere and their application to numerical computation of integrals” , Computing, Vol. 25, pp. 131–146
Freeden, W. (1984): “Spherical spline interpolation — basic theory and computational aspects” , J. Comput. Appl. Math. Vol.II, pp. 367–375
Wahba, G. (1981) :“Spline interpolation and smoothing on the sphere”, SIAM J. Sci. Stat. Comput. Vol. 2, pp. 5–16
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© 2001 Springer Science+Business Media New York
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Bezhaev, A.Y., Vasilenko, V.A. (2001). Reproducing Mappings and Characterization of Splines. In: Variational Theory of Splines. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3428-7_2
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DOI: https://doi.org/10.1007/978-1-4757-3428-7_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-3368-3
Online ISBN: 978-1-4757-3428-7
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