Geodesic
Splitting algorithms for the wavelet transform of first-degree splines on nonuniform grids
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 7, pp. 1236-1247 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For the splines of first degree with nonuniform knots, a new type of wavelets with a biased support is proposed. Using splitting with respect to the even and odd knots, a new wavelet decomposition algorithm in the form of the solution of a three-diagonal system of linear algebraic equations with respect to the wavelet coefficients is proposed. The application of the proposed implicit scheme to the point prediction of time series is investigated for the first time. Results of numerical experiments on the prediction accuracy and the compression of spline wavelet decompositions are presented. 
@article{ZVMMF_2016_56_7_a2,
     author = {B. M. Shumilov},
     title = {Splitting algorithms for the wavelet transform of first-degree splines on nonuniform grids},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1236--1247},
     year = {2016},
     volume = {56},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_7_a2/}
}
TY  - JOUR
AU  - B. M. Shumilov
TI  - Splitting algorithms for the wavelet transform of first-degree splines on nonuniform grids
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2016
SP  - 1236
EP  - 1247
VL  - 56
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_7_a2/
LA  - ru
ID  - ZVMMF_2016_56_7_a2
ER  - 
%0 Journal Article
%A B. M. Shumilov
%T Splitting algorithms for the wavelet transform of first-degree splines on nonuniform grids
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2016
%P 1236-1247
%V 56
%N 7
%U http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_7_a2/
%G ru
%F ZVMMF_2016_56_7_a2
B. M. Shumilov. Splitting algorithms for the wavelet transform of first-degree splines on nonuniform grids. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 56 (2016) no. 7, pp. 1236-1247. http://geodesic.mathdoc.fr/item/ZVMMF_2016_56_7_a2/

[1] Dobeshi I., Desyat lektsii po veivletam, Per. s angl., NITs «Regulyarnaya i khaoticheskaya dinamika», Izhevsk, 2001

[2] Lyche T., Mørken K., Pelosi F., “Stable, linear spline wavelets on nonuniform knots with vanishing moments”, Computer Aided Geometric Design, 26 (2009), 203–216 | DOI | MR | Zbl

[3] Sweldens W., Schröder P., “Building your own wavelets at home”, Wavelets in Computer Graphics, ACM SIGGRAPH Course notes, 1996, 15–87

[4] Sweldens W., “The lifting scheme: A custom-design construction of biorthogonal wavelets”, Appl. Comput. Harmonic Analys., 3:2 (1996), 186–200 | DOI | MR | Zbl

[5] Stolnits E., DeRouz T., Salezin D., Veivlety v kompyuternoi grafike, Per. s angl., NITs «Regulyarnaya i khaoticheskaya dinamika», Izhevsk, 2002, 272 pp.

[6] Koro K., Abe K., “Non-orthogonal spline wavelets for boundary element analysis”, Engng. Analys. with Boundary Elements, 25 (2001), 149–164 | DOI | Zbl

[7] Shumilov B. M., Matanov Sh. M., “Algoritm s rasschepleniem veivlet-preobrazovaniya splainov pervoi stepeni”, Vestn. Tomskogo gos. un-ta. Ser. Upravlenie, vychisl. tekhn. i informatika, 2011, no. 3, 51–57

[8] Shumilov B. M., Esharov E. A., Arkabaev N. K., “Postroenie i optimizatsiya prognozov na osnove rekurrentnykh splainov pervoi stepeni”, Sibirskii zh. vychisl. matem., 13:2 (2010), 227–241 | Zbl

[9] Demyanovich Yu. K., “Kalibrovochnoe sootnoshenie dlya V-splainov na neravnomernoi setke”, Matem. modelirovanie, 13:9 (2001), 98–100 | MR | Zbl

[10] Shumilov B. M., “Algoritm s rasschepleniem veivlet-preobrazovaniya ermitovykh kubicheskikh splainov”, Vestn. Tomskogo gos. un-ta. Ser. Matematika. Mekhanika, 2010, no. 4, 45–55 | MR

[11] Shumilov B. M., “Kubicheskie multiveivlety, ortogonalnye mnogochlenam, i algoritm s rasschepleniem”, Sibirskii zh. vychisl. matem., 16:3 (2013), 283–297

[12] Samarskii A. A., Nikolaev E. S., Metody resheniya setochnykh uravnenii, Nauka, M., 1978 | MR

[13] Novikov I. Ya., Protasov V. Yu., Skopina M. A., Teoriya vspleskov, Fizmatlit, M., 2006 | MR

[14] Lukashin Yu. P., Adaptivnye metody kratkosrochnogo prognozirovaniya vremennýkh ryadov, Finansy i statistika, M., 2003