Geodesic
Arithmetic complexity of the Stirling transforms
Diskretnaya Matematika, Tome 26 (2014) no. 4, pp. 23-35

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

For the linear Stirling transforms of both kinds, which are well-known in combinatorics, we obtain close to optimal estimates of the complexity of computation by vector addition chains and non-branching programs composed of arithmetic operations over real numbers. A relation between these problems and the Lagrange and Newton interpolation is discussed.
Keywords: Stirling transforms of the 1st and 2nd kinds, addition vector chains, circuits in arithmetic bases, the Lagrange and Newton interpolation, Vandermonde matrices, the Gauss $q$-binomial coefficient. 
@article{DM_2014_26_4_a2,
     author = {S. B. Gashkov},
     title = {Arithmetic complexity of the {Stirling} transforms},
     journal = {Diskretnaya Matematika},
     pages = {23--35},
     publisher = {mathdoc},
     volume = {26},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2014_26_4_a2/}
}
TY  - JOUR
AU  - S. B. Gashkov
TI  - Arithmetic complexity of the Stirling transforms
JO  - Diskretnaya Matematika
PY  - 2014
SP  - 23
EP  - 35
VL  - 26
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DM_2014_26_4_a2/
LA  - ru
ID  - DM_2014_26_4_a2
ER  - 
%0 Journal Article
%A S. B. Gashkov
%T Arithmetic complexity of the Stirling transforms
%J Diskretnaya Matematika
%D 2014
%P 23-35
%V 26
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DM_2014_26_4_a2/
%G ru
%F DM_2014_26_4_a2
S. B. Gashkov. Arithmetic complexity of the Stirling transforms. Diskretnaya Matematika, Tome 26 (2014) no. 4, pp. 23-35. http://geodesic.mathdoc.fr/item/DM_2014_26_4_a2/