Preprint
Error estimates for approximate approximations on compact intervals
Abstract
The aim of this paper is the investigation of the error which results from the method of approximate approximations applied to functions defined on compact in-tervals, only. This method, which is based on an approximate partition of unity, was introduced by V. Mazya in 1991 and has mainly been used for functions defied on the whole space up to now. For the treatment of differential equations and boundary integral equations, however, an efficient approximation procedure on compact intervals is needed.
In the present paper we apply the method of approximate approximations to functions which are defined on compact intervals. In contrast to the whole space case here a truncation error has to be controlled in addition. For the resulting total error pointwise estimates and L1-estimates are given, where all the constants are determined explicitly.
In the present paper we apply the method of approximate approximations to functions which are defined on compact intervals. In contrast to the whole space case here a truncation error has to be controlled in addition. For the resulting total error pointwise estimates and L1-estimates are given, where all the constants are determined explicitly.
Citation
@article{urn:nbn:de:hebis:34-200603298416,
author={Müller, Frank and Varnhorn, Werner},
title={Error estimates for approximate approximations on compact intervals},
year={2005}
}
0500 Oax 0501 Text $btxt$2rdacontent 0502 Computermedien $bc$2rdacarrier 1100 2005$n2005 1500 1/eng 2050 ##0##urn:nbn:de:hebis:34-200603298416 3000 Müller, Frank 3010 Varnhorn, Werner 4000 Error estimates for approximate approximations on compact intervals / Müller, Frank 4030 4060 Online-Ressource 4085 ##0##=u http://nbn-resolving.de/urn:nbn:de:hebis:34-200603298416=x R 4204 \$dPreprint 4170 Mathematische Schriften Kassel 7136 ##0##urn:nbn:de:hebis:34-200603298416
2006-03-29T14:09:36Z 2006-03-29T14:09:36Z 2005 urn:nbn:de:hebis:34-200603298416 http://hdl.handle.net/123456789/200603298416 181514 bytes application/pdf eng Urheberrechtlich geschützt https://rightsstatements.org/page/InC/1.0/ Approximate approximations Error estimates Gaussian kernels Approximationstheorie Fehlerabschätzung 510 Error estimates for approximate approximations on compact intervals Preprint The aim of this paper is the investigation of the error which results from the method of approximate approximations applied to functions defined on compact in-tervals, only. This method, which is based on an approximate partition of unity, was introduced by V. Mazya in 1991 and has mainly been used for functions defied on the whole space up to now. For the treatment of differential equations and boundary integral equations, however, an efficient approximation procedure on compact intervals is needed. In the present paper we apply the method of approximate approximations to functions which are defined on compact intervals. In contrast to the whole space case here a truncation error has to be controlled in addition. For the resulting total error pointwise estimates and L1-estimates are given, where all the constants are determined explicitly. open access Müller, Frank Varnhorn, Werner Mathematische Schriften Kassel 05, 20 Mathematische Schriften Kassel 05, 20
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