On Functionals Dual to Minimal Splines
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The paper considers minimal splines of Lagrange type of lower orders, and a system of functionals biorthogonal to the system of minimal coordinate splines is constructed. The results obtained are illustrated with an example of a polynomial generating vector function, which leads to the construction of B-splines from the approximation relations. Bibliography: 16 titles.
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- 1.M. J. Marsden and I. J. Schoenberg, “On variation diminishing spline approximation methods,” Mathematica (Cluj), 8 (31), No. 1, 61–82 (1966).Google Scholar
- 4.S. B. Stechkin and Yu. N. Subbotin, Splines in Computational Mathematics [in Russian], Moscow (1976).Google Scholar
- 5.Yu. S. Zav’yalov, V. I. Kvasov, and V. K. Miroshnichenko, Methods of Spline Functions [in Russian], Moscow 1980.Google Scholar
- 7.Yu. K. Dem’yanovich, Local Approximation on a Manifold and Minimal Splines [in Russian], St.Petersburg State University (1994).Google Scholar
- 8.I. G. Burova and Yu. K. Dem’yanovich, Minimal Splines and Their Applications [in Russian], St.Petersburg State University (2010).Google Scholar
- 11.Yu. K. Dem’yanovich and S. Yu. Marakova, “Solution of some interpolation problems in classes of minimal splines,” in: Numerical Analysis: Theory, Applications, Programs [in Russian], Moscow State Univ. (1999), pp. 131–153.Google Scholar
- 12.M. Spivak, Mathematical Analysis on Manifolds [in Russian], Lan’, St.Petersburg (2005).Google Scholar
- 14.A. A. Makarov, “Piecewise-continuous spline-wavelets on a nonuniform mesh,” Trudy SPIIRAN, 14, 103–131 (2010).Google Scholar
- 15.A. A. Makarov, “ A variant of spline-wavelet decomposition of spaces of the B-splines,” Vestn. St.Petersburg Univ., 10, vyp. 2, 59–71 (2009).Google Scholar
- 16.A. A. Makarov, “Biorthogonal functional systems and decomposition matrices for minimal splines,” Ukr. Mat. Visnik, 9, No. 2, 219–236 (2012).Google Scholar