Abstract
In the previous chapters we have already discussed the main theoretical questions concerning characterization formulae and convergence of variational splines. It is obvious now that there are certain numerical difficulties that arise in the construction and applications of the variational splines (for example, of multi-dimensional D m-splines on the scattered meshes) .
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Bibliography
Bezhaev, A. Yu., Vasilenko, V.A. (1987): “Splines in the Hilbert spaces and their finite element approximations” , in Sov. J. Numer. Math. Modelling, Vol. 2, No. 3, pp. 191–202 (VNU Science Press, Utrecht)
De Boor, C. (1978): “A Practical Guide to Splines” , Applied Math. Sciences, No. 27 (Springer Verlag)
Vasilenko, V.A. (1974): “Smoothing splines on subspaces and theorems of compactness” , in Chislennye metody mekhaniki sploshnoy sredi, Vol. 5, No. 5, pp. 37–42 (Ins. Theor. and Appl. Mech. Press, Novosibirsk) [in Russian]
Vasilenko, V.A. (1976): “Finite-dimensional approximation in least squared method” , in Variatsionno-raznostnye methody v matematicheskoy fizike, pp. 160–172 (Comp. Center Sib. Div. USSR Ac. Sci. Press, Novosibirsk) [in Russian]
Vasilenko, V.A. (1976): “Additional smoothness of spline-interpolants” , Preprint No. 24 (Comp. Center Sib. Div. USSR Ac. Sci. Press, Novosibirsk) [in Russian]
Vasilenko, V.A. (1978): “Numerical solution of prolongation problems by finite element method” , in Proc. of All-Union Conference on Finite Element Methods in Math. Physics, pp. 142–148 (Comp. Center Sib. Div. USSR Ac. Sci. Press, Novosibirsk) [in Russian]
Vasilenko, V.A. (1978): “Theory of Spline Functions” (Novosibirsk State Univ. Press, Novosibirsk) [in Russian]
Vasilenko, V.A. (1986) :“Spline Functions: Theory, Algorithms, Programs” (Optimization Software, New York)
Vasilenko, V.A., Zuzin, M.V., Kovalkov, A.V. (1984): “ Spline Functions and Digital Filters” (Comp. Center Sib. Div. USSR Ac. Sci. Press, Novosibirsk) [in Russian]
Vasilenko, V.A. (1984): “Error estimates in FEM for approximation of non-polynomial Dm-splines” , in Metod konechnykh elementov v nekotorikh zadachakh chislennogo analiza, pp. 21–30 (Comp. Center Sib. Div. USSR Ac. Sci. Press, Novosibirsk) [in Russian]
Vasilenko, V.A. (1986): “The finite element approximation of minimal surfaces” , in Vistas in Applied Mathematics: Numerical Analysis, Atmospheric Sciences, Immunology, pp. 181–189, (Optimization Software, New York)
Vasilenko, V.A., Rozhenko, A.J. (1989): “Discontinuity localization and spline approximation of discontinuous functions at the scattered meshes” , in Proc. of Int. Conf. on Numerical Methods and Applications, pp. 540–544 (Publ. House of Bulgarian Ac. Sci., Sofia)
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Bezhaev, A.Y., Vasilenko, V.A. (2001). Splines in Subspaces. In: Variational Theory of Splines. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3428-7_4
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DOI: https://doi.org/10.1007/978-1-4757-3428-7_4
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