Geodesic
Splines for three-point rational interpolants with autonomous poles
Daghestan Electronic Mathematical Reports, no. 7 (2017), pp. 16-28 Cet article a éte moissonné depuis la source Math-Net.Ru

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For arbitrary grids of nodes $\Delta: a=x_0$ $(N\geqslant 2)$ smooth splines for three–point rational interpolants are constructed, the poles of interpolants depend on nodes and the free parameter $\lambda$. Sequences of such splines and their derivatives for all functions $f(x)$ respectively of the classes of $C_{[a,b]}^{(i)}$ $(i=0,1,2)$ under the condition $\|\Delta\| \to 0$ uniformly in $[a,b]$ converge respectively to $f^{(i)}(x)$ $(i=0,1,2)$ (depending on the parameter $\lambda$). Bonds for the convergence rate are found in terms of the distance between the nodes.
Keywords: splines, rational splines.
Mots-clés : interpolation splines 
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A.-R. K. Ramazanov; V. G. Magomedova. Splines for three-point rational interpolants with autonomous poles. Daghestan Electronic Mathematical Reports, no. 7 (2017), pp. 16-28. http://geodesic.mathdoc.fr/item/DEMR_2017_7_a1/

[1] Alberg Dzh., Nilson E., Uolsh Dzh., Teoriya splainov i ee prilozheniya, Mir, M., 1972

[2] Stechkin S.B., Subbotin Yu.N., Dobavleniya k knige Dzh. Alberg, E. Nilson, Dzh. Uolsh. Teoriya splainov i ee prilozheniya, Mir, M., 1972 | MR

[3] Stechkin S.B., Subbotin Yu.N., Splainy v vychislitelnoi matematike, Nauka, M., 1976 | MR

[4] Korneichuk N.P., Splainy v teorii priblizheniya, Nauka, M., 1984 | MR

[5] Malozemov V.N., Pevnyi A.B., Polinomialnye splainy, Izd-vo LGU, L., 1986

[6] Zavyalov Yu.S., Kvasov B.I.,Miroshnichenko V.L., Metody splain–funktsii, Nauka, M., 1980 | MR

[7] Subbotin Yu.N., “Variatsii na temu splainov”, Fundament. i prikl. matem., 3:4 (1997), 1043–1058 | MR | Zbl

[8] Nord S., “Approximation properties of the spline fit”, BIT., 7 (1967), 132–144 | DOI | MR | Zbl

[9] Privalov Al.A., “O skhodimosti kubicheskikh interpolyatsionnykh splainov k nepreryvnoi funktsii”, Matem. zametki, 25:5 (1979), 681–700 | MR | Zbl

[10] Ramazanov A.-R.K., Magomedova V.G., “Splainy po ratsionalnym interpolyantam”, Dagestanskie Elektronnye Matematicheskie Izvestiya., 2015, no. 4, 22–31 | MR

[11] Ramazanov A.-R.K., Magomedova V.G., “Splainy po chetyrekhtochechnym ratsionalnym interpolyantam”, Tr. In-ta matematiki i mekhaniki UrO RAN., 22:4 (2016), 233–246 | MR