Interpolation operators on the space of holomorphic functions on the unit circle
Applications of Mathematics (2001)
- Volume: 46, Issue: 3, page 161-189
- ISSN: 0862-7940
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topKofroň, Josef. "Interpolation operators on the space of holomorphic functions on the unit circle." Applications of Mathematics 46.3 (2001): 161-189. <http://eudml.org/doc/33082>.
@article{Kofroň2001,
abstract = {The aim of the paper is to get an estimation of the error of the general interpolation rule for functions which are real valued on the interval $[-a,a]$, $a\in (0,1)$, have a holomorphic extension on the unit circle and are quadratic integrable on the boundary of it. The obtained estimate does not depend on the derivatives of the function to be interpolated. The optimal interpolation formula with mutually different nodes is constructed and an error estimate as well as the rate of convergence are obtained. The general extremal problem with free weights and knots is solved.},
author = {Kofroň, Josef},
journal = {Applications of Mathematics},
keywords = {numerical interpolation; optimal interpolatory rule with prescribed nodes; optimal interpolatory rule with free nodes; remainder estimation; numerical interpolation; optimal interpolatory rule with prescribed nodes; optimal interpolatory rule with free nodes; remainder estimation},
language = {eng},
number = {3},
pages = {161-189},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Interpolation operators on the space of holomorphic functions on the unit circle},
url = {http://eudml.org/doc/33082},
volume = {46},
year = {2001},
}
TY - JOUR
AU - Kofroň, Josef
TI - Interpolation operators on the space of holomorphic functions on the unit circle
JO - Applications of Mathematics
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 46
IS - 3
SP - 161
EP - 189
AB - The aim of the paper is to get an estimation of the error of the general interpolation rule for functions which are real valued on the interval $[-a,a]$, $a\in (0,1)$, have a holomorphic extension on the unit circle and are quadratic integrable on the boundary of it. The obtained estimate does not depend on the derivatives of the function to be interpolated. The optimal interpolation formula with mutually different nodes is constructed and an error estimate as well as the rate of convergence are obtained. The general extremal problem with free weights and knots is solved.
LA - eng
KW - numerical interpolation; optimal interpolatory rule with prescribed nodes; optimal interpolatory rule with free nodes; remainder estimation; numerical interpolation; optimal interpolatory rule with prescribed nodes; optimal interpolatory rule with free nodes; remainder estimation
UR - http://eudml.org/doc/33082
ER -
References
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