Use of Divided Differences and $B$ Splines for Constructing Fast Discrete Transforms of Wavelet Type on Nonuniform Grids
Matematičeskie zametki, Tome 77 (2005) no. 5, pp. 743-752.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we construct fast discrete transforms of wavelet type with an arbitrary number of zero moments for nonuniform grids. We obtain explicit formulas for the parameters defining the wavelet transform.
@article{MZM_2005_77_5_a8,
     author = {I. V. Oseledets},
     title = {Use of {Divided} {Differences} and $B$ {Splines} for {Constructing} {Fast} {Discrete} {Transforms} of {Wavelet} {Type} on {Nonuniform} {Grids}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {743--752},
     publisher = {mathdoc},
     volume = {77},
     number = {5},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_77_5_a8/}
}
TY  - JOUR
AU  - I. V. Oseledets
TI  - Use of Divided Differences and $B$ Splines for Constructing Fast Discrete Transforms of Wavelet Type on Nonuniform Grids
JO  - Matematičeskie zametki
PY  - 2005
SP  - 743
EP  - 752
VL  - 77
IS  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2005_77_5_a8/
LA  - ru
ID  - MZM_2005_77_5_a8
ER  - 
%0 Journal Article
%A I. V. Oseledets
%T Use of Divided Differences and $B$ Splines for Constructing Fast Discrete Transforms of Wavelet Type on Nonuniform Grids
%J Matematičeskie zametki
%D 2005
%P 743-752
%V 77
%N 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2005_77_5_a8/
%G ru
%F MZM_2005_77_5_a8
I. V. Oseledets. Use of Divided Differences and $B$ Splines for Constructing Fast Discrete Transforms of Wavelet Type on Nonuniform Grids. Matematičeskie zametki, Tome 77 (2005) no. 5, pp. 743-752. http://geodesic.mathdoc.fr/item/MZM_2005_77_5_a8/

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

[2] Chui K., Vvedenie v veivlety, Mir, M., 2001

[3] Vasilenko V. A., Splain-funktsii: teoriya, algoritmy, programmy, Nauka, Novosibirsk, 1983

[4] Sweldens W., “The lifting scheme: A custom design construction of biorthogonal wavelets”, Industrial Mathematics Initiative, 7, University of South Carolina, 1994

[5] Akopyan A. A., Saakyan A. A., “Mnogomernye splainy i polinomialnaya interpolyatsiya”, UMN, 48:5 (1993), 3–76 | MR | Zbl

[6] Daubechies I., “Orthonormal bases of compactly supported wavelets”, Comm. of Pure and Appl. Math., 41 (7) (1988), 990–996