Geodesic
Local interpolation curve with a prescribed degree of smoothness which preserves the constant sign of curvature
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 2, pp. 290-300 
I. A. Rumyantsev. Local interpolation curve with a prescribed degree of smoothness which preserves the constant sign of curvature. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 23 (1983) no. 2, pp. 290-300. http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_2_a4/
@article{ZVMMF_1983_23_2_a4,
     author = {I. A. Rumyantsev},
     title = {Local interpolation curve with a prescribed degree of smoothness which preserves the constant sign of curvature},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {290--300},
     year = {1983},
     volume = {23},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_2_a4/}
}
TY  - JOUR
AU  - I. A. Rumyantsev
TI  - Local interpolation curve with a prescribed degree of smoothness which preserves the constant sign of curvature
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 1983
SP  - 290
EP  - 300
VL  - 23
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_2_a4/
LA  - ru
ID  - ZVMMF_1983_23_2_a4
ER  - 
%0 Journal Article
%A I. A. Rumyantsev
%T Local interpolation curve with a prescribed degree of smoothness which preserves the constant sign of curvature
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 1983
%P 290-300
%V 23
%N 2
%U http://geodesic.mathdoc.fr/item/ZVMMF_1983_23_2_a4/
%G ru
%F ZVMMF_1983_23_2_a4

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

A local interpolation method is described, whereby the curve is kept monotonic and its curvature sign fixed, provided that the initial points enable such a curve to be constructed. The algorithm allows the straight parts on the curve to be separated and provides continuity of the derivatives of a given degree. It is shown that, if the function $f^{(q)}(x)$ is continuous in the interval $[a,b]$, $q=0,1,2$, then the interpolation function of the appropriate degree of smoothness converges to the function $f(x)$ on a sequence of meshesat least at the rat $\|\Delta\|^q$, where $\|\Delta\|=\max_i|\Delta x_i|$.