Geodesic
Recursive interpolation by cubic splines with additional nodes
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 2, pp. 179-185 Cet article a éte moissonné depuis la source Math-Net.Ru

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A method, designed for systems operating in real time, is proposed for recursive construction of cubic interpolatory splines with additional nodes – the points of discontinuity of the third derivative of the spline. It is proved that the method converges to the function being interpolated, to fourth order of accuracy with respect to the maximum distance between the data points of the function. 
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B. M. Shumilov. Recursive interpolation by cubic splines with additional nodes. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 30 (1990) no. 2, pp. 179-185. http://geodesic.mathdoc.fr/item/ZVMMF_1990_30_2_a0/

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

[2] Grebennikov A. I., Metod splainov i reshenie nekorrektnykh zadach teorii priblizhenii, Izd-vo MGU, M., 1983 | MR | Zbl

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

[4] Goldenberg L. M., Klimontov V. E., Seredinskii A. V., “Rekurrentnye metody postroeniya interpolyatsionnykh splain-funktsii”, Avtomatika i telemekhan., 1979, no. 3, 173–176 | MR

[5] Kvasov B. I., “Parabolicheskie $X$-splainy”, Metody splain-funktsii v chisl. analize, Vychisl. sistemy, 98, Novosibirsk, 1983, 3–19 | MR | Zbl

[6] Shumilov B. M., “Lagranzheva interpolyatsiya kubicheskimi splainami s dopolnitelnymi uzlami”, Priblizhenie splainami, Vychisl. sistemy, 106, Novosibirsk, 1984, 29–40 | MR | Zbl

[7] Shumilov B. M., “O lagranzhevoi interpolyatsii parabolicheskimi splainami s dopolnitelnymi uzlami”, Izv. vuzov. Matematika, 1987, no. 1(296), 9–12 | MR