Geodesic
Interpolation formulas for functions of exponential type
Applications of Mathematics, Tome 46 (2001) no. 6, pp. 401-417.

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

In the paper we present a derivative-free estimate of the remainder of an arbitrary interpolation rule on the class of entire functions which, moreover, belong to the space $L^2_{(-\infty ,+\infty )}$. The theory is based on the use of the Paley-Wiener theorem. The essential advantage of this method is the fact that the estimate of the remainder is formed by a product of two terms. The first term depends on the rule only while the second depends on the interpolated function only. The obtained estimate of the remainder of Lagrange’s rule shows the efficiency of the method of estimate. The first term of the estimate is a starting point for the construction of the optimal rule; only the optimal rule with prescribed nodes of the interpolatory rule is investigated. An example illustrates the developed theory.
DOI : 10.1023/A:1013760511662
Classification : 41A05, 41A50, 41A80, 65D05
Keywords: entire functions; Paley-Wiener theorem; numerical interpolation; optimal interpolatory rule with prescribed nodes; remainder estimate 
@article{10_1023_A_1013760511662,
     author = {Kofro\v{n}, Josef and Moravcov\'a, Em{\'\i}lie},
     title = {Interpolation formulas for functions of exponential type},
     journal = {Applications of Mathematics},
     pages = {401--417},
     publisher = {mathdoc},
     volume = {46},
     number = {6},
     year = {2001},
     doi = {10.1023/A:1013760511662},
     mrnumber = {1865514},
     zbl = {1065.65011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1023/A:1013760511662/}
}
TY  - JOUR
AU  - Kofroň, Josef
AU  - Moravcová, Emílie
TI  - Interpolation formulas for functions of exponential type
JO  - Applications of Mathematics
PY  - 2001
SP  - 401
EP  - 417
VL  - 46
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1023/A:1013760511662/
DO  - 10.1023/A:1013760511662
LA  - en
ID  - 10_1023_A_1013760511662
ER  - 
%0 Journal Article
%A Kofroň, Josef
%A Moravcová, Emílie
%T Interpolation formulas for functions of exponential type
%J Applications of Mathematics
%D 2001
%P 401-417
%V 46
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1023/A:1013760511662/
%R 10.1023/A:1013760511662
%G en
%F 10_1023_A_1013760511662
Kofroň, Josef; Moravcová, Emílie. Interpolation formulas for functions of exponential type. Applications of Mathematics, Tome 46 (2001) no. 6, pp. 401-417. doi : 10.1023/A:1013760511662. http://geodesic.mathdoc.fr/articles/10.1023/A:1013760511662/

Cité par Sources :