Geodesic
Shape preserving conditions for quadratic spline interpolation in the sense of Subbotin and Marsden
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 4, pp. 145-152 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

For two constructions of quadratic interpolation splines in the sense of Subbotin and Marsden, simple sufficient conditions are established under which the interpolant inherits the geometric properties (positivity, monotonicity, and convexity) of the interpolated data.
Keywords: quadratic spline, shape preservation.
Mots-clés : interpolation 
@article{TIMM_2012_18_4_a12,
     author = {Yu. S. Volkov and V. T. Shevaldin},
     title = {Shape preserving conditions for quadratic spline interpolation in the sense of {Subbotin} and {Marsden}},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {145--152},
     year = {2012},
     volume = {18},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2012_18_4_a12/}
}
TY  - JOUR
AU  - Yu. S. Volkov
AU  - V. T. Shevaldin
TI  - Shape preserving conditions for quadratic spline interpolation in the sense of Subbotin and Marsden
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2012
SP  - 145
EP  - 152
VL  - 18
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/TIMM_2012_18_4_a12/
LA  - ru
ID  - TIMM_2012_18_4_a12
ER  - 
%0 Journal Article
%A Yu. S. Volkov
%A V. T. Shevaldin
%T Shape preserving conditions for quadratic spline interpolation in the sense of Subbotin and Marsden
%J Trudy Instituta matematiki i mehaniki
%D 2012
%P 145-152
%V 18
%N 4
%U http://geodesic.mathdoc.fr/item/TIMM_2012_18_4_a12/
%G ru
%F TIMM_2012_18_4_a12
Yu. S. Volkov; V. T. Shevaldin. Shape preserving conditions for quadratic spline interpolation in the sense of Subbotin and Marsden. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 4, pp. 145-152. http://geodesic.mathdoc.fr/item/TIMM_2012_18_4_a12/

[1] Subbotin Yu. N., “O kusochno polinomialnoi interpolyatsii”, Mat. zametki, 1:1 (1967), 63–70 | MR | Zbl

[2] Stechkin S. B., Subbotin Yu. N., “Dobavleniya”: Dzh. Alberg, E. Nilson, Dzh. Uolsh, Teoriya splainov i ee prilozheniya, Mir, M., 1972, 270–309 | MR

[3] Stechkin S. B., Subbotin Yu. N., Splainy v vychislitelnoi matematike, Nauka, M., 1976, 248 pp. | MR | Zbl

[4] Marsden M., “Quadratic spline interpolation”, Bull. Amer. Math. Soc., 80:5 (1974), 903–906 | DOI | MR | Zbl

[5] Marsden M., “Operator norm bounds and error bounds for quadratic spline interpolation”, Approximation theory, Papers, VIth Semester (Stefan Banach Internat. Math. Center, Warszawa, 1975), Banach Center Publ., 4, PWN – Polish Scientific Publishers, Warsaw, 1979, 159–175 | MR

[6] Volkov Yu. S., Dve konstruktsii interpolyatsionnykh splainov chetnoi stepeni, Preprint No 169, In-t matematiki im. S. L. Soboleva SO RAN, Novosibirsk, 2006, 32 pp.

[7] Volkov Yu. S., “O postroenii interpolyatsionnykh polinomialnykh splainov”, Splain-funktsii i ikh prilozheniya, Vychisl. sistemy, 159, IM SO RAN, Novosibirsk, 1997, 3–18 | MR

[8] Volkov Yu. S., “O monotonnoi interpolyatsii kubicheskimi splainami”, Vychisl. tekhnologii, 6:6 (2001), 14–24 | MR | Zbl

[9] Volkov Yu. S., “Novyi sposob postroeniya interpolyatsionnykh kubicheskikh splainov”, Zhurn. vychisl. matematiki i mat. fiziki, 44:2 (2004), 231–241 | MR | Zbl

[10] Volkov Yu. S., Bogdanov V. V., Miroshnichenko V. L., Shevaldin V. T., “Formosokhranyayuschaya interpolyatsiya kubicheskimi splainami”, Mat. zametki, 88:6 (2010), 836–844 | DOI | MR | Zbl

[11] Miroshnichenko V. L., “Convex and monotone spline interpolation”, Constructive theory of function, Proc. Intern. Conf. (Varna, 1984), Publishing House of Bulgarian Academy of Sciences, Sofia, 1984, 610–620

[12] Subbotin Yu. N., “Nasledovanie svoistv monotonnosti i vypuklosti pri lokalnoi approksimatsii”, Zhurn. vychisl. matematiki i mat. fiziki, 33:7 (1993), 996–1003 | MR | Zbl

[13] Shevaldin V. T., “Approksimatsiya lokalnymi parabolicheskimi splainami s proizvolnym raspolozheniem uzlov”, Sib. zhurn. vychisl. matematiki, 8:1 (2005), 77–88 | Zbl

[14] Subbotin Yu. N., “Approksimatsii polinomialnymi i trigonometricheskimi splainami tretego poryadka, sokhranyayuschie nekotorye svoistva approksimiruemykh funktsii”, Tr. In-ta matematiki i mekhaniki UrO RAN, 13, no. 2, 2007, 156–166

[15] Volkov Yu. S., Strelkova E. V., Shevaldin V. T., “Lokalnaya approksimatsiya splainami so smescheniem uzlov”, Mat. trudy, 14:2 (2011), 73–82 | MR

[16] Alberg Dzh., Nilson E., Uolsh Dzh., Teoriya splainov i ee prilozheniya, Mir, M., 1972, 316 pp. | MR | Zbl

[17] Subbotin Yu. N., “Ekstremalnye zadachi funktsionalnoi interpolyatsii i interpolyatsionnye v srednem splainy”, Priblizhenie funktsii i operatorov, Tr. MIAN SSSR, 138, 1975, 118–173 | MR | Zbl

[18] Bogdanov V. V., Volkov Yu. S., “Vybor parametrov obobschennykh kubicheskikh splainov pri vypukloi interpolyatsii”, Sib. zhurn. vychisl. matematiki, 9:1 (2006), 5–22 | Zbl

[19] Kindalev B. S., “Asymptotics of error for interpolating splines of even degree”, Constructive theory of function, Proceed. Intern. Conf. (Varna, 1984), Publishing House of Bulgarian Academy of Sciences, Sofia, 1984, 445–450

[20] Volkov Yu. S., Miroshnichenko V. L., “O priblizhenii proizvodnykh skachkom interpolyatsionnogo splaina”, Mat. zametki, 89:1 (2011), 127–130 | DOI | MR | Zbl

[21] Miroshnichenko V. L., “Dostatochnye usloviya monotonnosti i vypuklosti dlya interpolyatsionnykh parabolicheskikh splainov”, Splainy i ikh prilozheniya, Vychisl. sistemy, 142, IM SOAN SSSR, Novosibirsk, 1991, 3–14 | MR