Interpolation formulas for functions of exponential type

Kofroň, Josef, and Moravcová, Emílie. "Interpolation formulas for functions of exponential type." Applications of Mathematics 46.6 (2001): 401-417. <http://eudml.org/doc/33094>.

@article{Kofroň2001,
abstract = {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.},
author = {Kofroň, Josef, Moravcová, Emílie},
journal = {Applications of Mathematics},
keywords = {entire functions; Paley-Wiener theorem; numerical interpolation; optimal interpolatory rule with prescribed nodes; remainder estimate; entire functions; Paley-Wiener theorem; numerical interpolation; optimal interpolatory rule with prescribed nodes; remainder estimation},
language = {eng},
number = {6},
pages = {401-417},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Interpolation formulas for functions of exponential type},
url = {http://eudml.org/doc/33094},
volume = {46},
year = {2001},
}

TY - JOUR
AU - Kofroň, Josef
AU - Moravcová, Emílie
TI - Interpolation formulas for functions of exponential type
JO - Applications of Mathematics
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 46
IS - 6
SP - 401
EP - 417
AB - 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.
LA - eng
KW - entire functions; Paley-Wiener theorem; numerical interpolation; optimal interpolatory rule with prescribed nodes; remainder estimate; entire functions; Paley-Wiener theorem; numerical interpolation; optimal interpolatory rule with prescribed nodes; remainder estimation
UR - http://eudml.org/doc/33094
ER -