An algorithm with splitting of the wavelet transform of Hermitian cubic splines
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 4 (2010), pp. 45-55 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper an implicit method for the decomposition of Hermitian cubic spline wavelets is investigated. A parallel algorithm of the wavelet transform of Hermitian cubic splines has been found as a solution of two three-diagonal systems of linear equations with a dominating principal diagonal by use of splitting with respect to the even and odd mesh points.
Keywords: Hermitian splines, wavelets, relations of decomposition and restoration.
@article{VTGU_2010_4_a4,
     author = {B. M. Shumilov},
     title = {An algorithm with splitting of the wavelet transform of {Hermitian} cubic splines},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {45--55},
     year = {2010},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2010_4_a4/}
}
TY  - JOUR
AU  - B. M. Shumilov
TI  - An algorithm with splitting of the wavelet transform of Hermitian cubic splines
JO  - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
PY  - 2010
SP  - 45
EP  - 55
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VTGU_2010_4_a4/
LA  - ru
ID  - VTGU_2010_4_a4
ER  - 
%0 Journal Article
%A B. M. Shumilov
%T An algorithm with splitting of the wavelet transform of Hermitian cubic splines
%J Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
%D 2010
%P 45-55
%N 4
%U http://geodesic.mathdoc.fr/item/VTGU_2010_4_a4/
%G ru
%F VTGU_2010_4_a4
B. M. Shumilov. An algorithm with splitting of the wavelet transform of Hermitian cubic splines. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 4 (2010), pp. 45-55. http://geodesic.mathdoc.fr/item/VTGU_2010_4_a4/

[1] Dobeshi I., Desyat lektsii po veivletam, per. s angl., NITs “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2001, 332 pp.

[2] Chui Ch., Vvedenie v veivlety, per. s angl., Mir, M., 2001, 412 pp.

[3] Stolnits E., DeRouz T., Salezin D., Veivlety v kompyuternoi grafike, per. s angl., NITs “Regulyarnaya i khaoticheskaya dinamika”, Izhevsk, 2002, 272 pp.

[4] Dahmen W., Han B., Jia R.-Q., Kunoth A., “Biorthogonal multiwavelets on the interval: cubic Hermite splines”, Constr. Approx., 16 (2000), 221–259 | DOI | MR | Zbl

[5] Han B., “Approximation properties and construction of Hermite interpolants and biorthogonal multiwavelets”, J. Approxim. Theory, 110 (2001), 18–53 | DOI | MR | Zbl

[6] Popova O. O., Ruchkina Yu. Yu., Shumilov B. M., “Postroenie sistemy bazisnykh veivletov Ermita dlya sluchaya neravnomernoi setki”, 4-ya Vseros. nauch.-praktich. konf. studentov “Molodezh i sovremennye informatsionnye tekhnologii”, TPU, Tomsk, 2006, 37–38

[7] Jia R.-Q., Liu S.-T., “Wavelet bases of Hermite cubic splines on the interval”, Advances Computational Mathematics, 25 (2006), 23–39 | DOI | MR | Zbl

[8] Shumilov B. M., Esharov E. A., “Postroenie ermitovykh splain-veivletov”, Vestnik Tomskogo gosudarstvennogo universiteta. Prilozhenie, 2006, no. 19, 260–266

[9] Zavyalov Yu. S., Kvasov B. I., Miroshnichenko V. L., Metody splain-funktsii, Nauka, M., 1980, 352 pp. | MR

[10] Heil C., Strang G., Strela V., “Approximation by translate of refinable functions”, Numer. Math., 73 (1996), 75–94 | DOI | MR | Zbl

[11] Maleknejad K., Youse M., “Numerical solution of the integral equation of the second kind by using wavelet bases of Hermite cubic splines”, Applied Mathematics and Computation, 183 (2006), 134–141 | DOI | MR | Zbl

[12] Zhao G., Xu S., Li W., Zhu X., “Wavelets-based multiresolution representation and manipulation of closed $B$-spline curves”, Proceedings of IC-SEC, 2002, 490–493

[13] Shumilov B. M., Esharov E. A., “Nestatsionarnye splain-veivlety v GIS i SAPR lineino-protyazhennykh prostranstvennykh ob'ektov”, Vestnik Tomskogo gosudarstvennogo arkhitekturno-stroitelnogo universiteta, 2006, no. 1(12), 153–163

[14] Tursunov D. A., Shumilov B. M., Esharov E. A., Tursunov E. A., “Novyi tip ermitovykh multiveivletov pyatoi stepeni”, Pyataya Sibirskaya konferentsiya po parallelnym i vysokoproizvoditelnym vychisleniyam, Programma i tezisy dokladov (1–3 dekabrya 2009 g.), Izd-vo Tom. un-ta, Tomsk, 2009, 57–58