Geodesic
On calculation of scalar products of $B$-splines
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 9 (2006) no. 1, pp. 55-61 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The paper is devoted to algorithms of stable calculation of scalar products of $B$-splines. A new modification of recursive calculations of integrals in the Gram matrix is proposed. The modified algorithm is nearly two times faster than the Gauss quadratures and the full recursion algorithm. 
@article{SJVM_2006_9_1_a5,
     author = {A. I. Rozhenko},
     title = {On calculation of scalar products of $B$-splines},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {55--61},
     year = {2006},
     volume = {9},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2006_9_1_a5/}
}
TY  - JOUR
AU  - A. I. Rozhenko
TI  - On calculation of scalar products of $B$-splines
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2006
SP  - 55
EP  - 61
VL  - 9
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SJVM_2006_9_1_a5/
LA  - ru
ID  - SJVM_2006_9_1_a5
ER  - 
%0 Journal Article
%A A. I. Rozhenko
%T On calculation of scalar products of $B$-splines
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2006
%P 55-61
%V 9
%N 1
%U http://geodesic.mathdoc.fr/item/SJVM_2006_9_1_a5/
%G ru
%F SJVM_2006_9_1_a5
A. I. Rozhenko. On calculation of scalar products of $B$-splines. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 9 (2006) no. 1, pp. 55-61. http://geodesic.mathdoc.fr/item/SJVM_2006_9_1_a5/

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

[2] Vasilenko V. A., Splain-funktsii: teoriya, algoritmy, programmy, Nauka. Sib. otd-nie, Novosibirsk, 1983 | MR

[3] Rozhenko A. I., Abstraktnaya teoriya splainov: Ucheb. posobie, Izd. tsentr NGU, Novosibirsk, 1999

[4] de Boor C., Lyche T., Schumaker L. L., “On calculating with B-splines. II. Integration”, Numerische Methoden der Approximations Theorie, Vol. 3, Int. Ser. Num. Math., 30, Birkhäuser, Basel, 1976, 123–146 | MR

[5] Vermeulen A. H., Bartels R. H., Heppler G. R., “Integrating products of B-splines”, SIAM J. Sci. Stat. Comput., 13:4 (1992), 1025–1038 | DOI | MR | Zbl