Form preservation under approximation by local exponential splines of an arbitrary order
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 291-299
Voir la notice de l'article provenant de la source Math-Net.Ru
We continue the study of the properties of local $\mathcal L$-splines with uniform knots (such splines were constructed in the authors' earlier papers) corresponding to a linear differential operator $\mathcal L$ of order $r$ with constant coefficients and real pairwise distinct roots of the characteristic polynomial. Sufficient conditions (which are also necessary) are established under which the $\mathcal L$-spline locally inherits the property of the generalized $k$-monotonicity of $(k\le r-1)$ input data, which are the values of the approximated function at the nodes of a uniform grid shifted with respect to the grid of knots of the $\mathcal L$-spline. The parameters of an $\mathcal L$-spline that is exact on the kernel of the operator $\mathcal L$ are written explicitly.
Keywords:
form preservation, $k$-monotonicity, local $\mathcal L$-spline.
@article{TIMM_2011_17_3_a28,
author = {E. V. Strelkova and V. T. Shevaldin},
title = {Form preservation under approximation by local exponential splines of an arbitrary order},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {291--299},
publisher = {mathdoc},
volume = {17},
number = {3},
year = {2011},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a28/}
}
TY - JOUR AU - E. V. Strelkova AU - V. T. Shevaldin TI - Form preservation under approximation by local exponential splines of an arbitrary order JO - Trudy Instituta matematiki i mehaniki PY - 2011 SP - 291 EP - 299 VL - 17 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a28/ LA - ru ID - TIMM_2011_17_3_a28 ER -
%0 Journal Article %A E. V. Strelkova %A V. T. Shevaldin %T Form preservation under approximation by local exponential splines of an arbitrary order %J Trudy Instituta matematiki i mehaniki %D 2011 %P 291-299 %V 17 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a28/ %G ru %F TIMM_2011_17_3_a28
E. V. Strelkova; V. T. Shevaldin. Form preservation under approximation by local exponential splines of an arbitrary order. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 291-299. http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a28/