Geodesic
A~Criterion for the Uniform Convergence of the Lagrange--Jacobi Interpolation Process
Matematičeskie zametki, Tome 79 (2006) no. 2, pp. 254-266

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

We obtain a uniform and sufficient condition for the convergence of the Lagrange interpolation process with Jacobi nodes on a closed interval $[a,b]\subset(-1,1)$. The condition is stated in terms of the second differences of the interpolated function and uses its values only at the interpolation nodes. Some well-known criteria for uniform convergence are obtained as a consequence of our result. 
@article{MZM_2006_79_2_a8,
     author = {V. V. Novikov},
     title = {A~Criterion for the {Uniform} {Convergence} of the {Lagrange--Jacobi} {Interpolation} {Process}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {254--266},
     publisher = {mathdoc},
     volume = {79},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a8/}
}
TY  - JOUR
AU  - V. V. Novikov
TI  - A~Criterion for the Uniform Convergence of the Lagrange--Jacobi Interpolation Process
JO  - Matematičeskie zametki
PY  - 2006
SP  - 254
EP  - 266
VL  - 79
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a8/
LA  - ru
ID  - MZM_2006_79_2_a8
ER  - 
%0 Journal Article
%A V. V. Novikov
%T A~Criterion for the Uniform Convergence of the Lagrange--Jacobi Interpolation Process
%J Matematičeskie zametki
%D 2006
%P 254-266
%V 79
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a8/
%G ru
%F MZM_2006_79_2_a8
V. V. Novikov. A~Criterion for the Uniform Convergence of the Lagrange--Jacobi Interpolation Process. Matematičeskie zametki, Tome 79 (2006) no. 2, pp. 254-266. http://geodesic.mathdoc.fr/item/MZM_2006_79_2_a8/