Multiwavelets of the third degree Hermitian splines, orthogonal to cubic polynomials
Matematičeskoe modelirovanie, Tome 25 (2013) no. 4, pp. 17-28.

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

For a case of Hermitian splines of the third degree the new type multiwavelets with the reduced support is offered. Their advantage to compression of numerical data in comparison with known type cubic multiwavelets is proved. Results of numerical experiments are presented.
Keywords: Hermitian splines of the third degree, multiwavelets, orthogonality to polynomials.
@article{MM_2013_25_4_a1,
     author = {B. M. Shumilov},
     title = {Multiwavelets of the third degree {Hermitian} splines, orthogonal to cubic polynomials},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {17--28},
     publisher = {mathdoc},
     volume = {25},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2013_25_4_a1/}
}
TY  - JOUR
AU  - B. M. Shumilov
TI  - Multiwavelets of the third degree Hermitian splines, orthogonal to cubic polynomials
JO  - Matematičeskoe modelirovanie
PY  - 2013
SP  - 17
EP  - 28
VL  - 25
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2013_25_4_a1/
LA  - ru
ID  - MM_2013_25_4_a1
ER  - 
%0 Journal Article
%A B. M. Shumilov
%T Multiwavelets of the third degree Hermitian splines, orthogonal to cubic polynomials
%J Matematičeskoe modelirovanie
%D 2013
%P 17-28
%V 25
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2013_25_4_a1/
%G ru
%F MM_2013_25_4_a1
B. M. Shumilov. Multiwavelets of the third degree Hermitian splines, orthogonal to cubic polynomials. Matematičeskoe modelirovanie, Tome 25 (2013) no. 4, pp. 17-28. http://geodesic.mathdoc.fr/item/MM_2013_25_4_a1/

[1] Strela V., Multiwavelets: Theory and Applications, Submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics, Massachusetts Institute of Technology, 1996, 99 pp. | MR

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

[3] Warming R., Beam R., “Discrete multiresolution analysis using Hermite interpolation: Biorthogonal multiwavelets”, SIAM J. Sci. Comp., 22:1 (2000), 269–317 | MR

[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] Zhang Qin-li, Wu Bo-ying, He Chun-jiang, “Hermite multiwavelets”, Harbin gongue daxue xuebao [J. Harbin Inst.Technol.], 36:6 (2004), 787–789 | MR | Zbl

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

[8] Dobeshi I., Desyat lektsii po veivletam, Per. s angl., NITs «Regulyarnaya i khaoticheskaya dinamika», Izhevsk, 2001, 332 pp.

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

[10] Novikov I. Ya., Protasov V. Yu., Skopina M. A., Teoriya vspleskov, Fizmatlit, M., 2006, 616 pp. | MR

[11] 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

[12] Koro K., Ade K., “Non-orthogonal spline wavelets for boundary element analysis”, Engineering Analysis with Boundary Elements, 25 (2001), 149–164 | DOI | Zbl

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

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

[15] Arandiga F., Baeza A., Donat R., “Discrete multiresolution based on hermite interpolation: computing derivatives”, Communications in Nonlinear Science and Numerical Simulation, 9 (2004), 263–273 | DOI | MR | Zbl

[16] Shumilov B. M., “Algoritm s rasschepleniem veivlet-preobrazovaniya ermitovykh kubicheskikh splainov”, Vestnik Tomskogo gosudarstvennogo universiteta. Ser. Matematika. Mekhanika, 2010, no. 4(12), 45–55