External estimation of a segment function by a polynomial strip
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 7, pp. 1175-1183
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The problem is considered of constructing a least-width strip with a polynomial axis that contains the graph of a given continuous segment function. Convex analysis methods are used to obtain a criterion for solving the problem in a form comparable to the Chebyshev alternance. Sufficient conditions for the uniqueness of a solution are given, including those taking into account the differential properties of the segment function to be estimated.
@article{ZVMMF_2009_49_7_a4,
author = {I. Yu. Vygodchikova and S. I. Dudov and E. V. Sorina},
title = {External estimation of a~segment function by a~polynomial strip},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1175--1183},
publisher = {mathdoc},
volume = {49},
number = {7},
year = {2009},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_7_a4/}
}
TY - JOUR AU - I. Yu. Vygodchikova AU - S. I. Dudov AU - E. V. Sorina TI - External estimation of a segment function by a polynomial strip JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2009 SP - 1175 EP - 1183 VL - 49 IS - 7 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_7_a4/ LA - ru ID - ZVMMF_2009_49_7_a4 ER -
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I. Yu. Vygodchikova; S. I. Dudov; E. V. Sorina. External estimation of a segment function by a polynomial strip. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 7, pp. 1175-1183. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_7_a4/