A numerical experiment related to Zolotarev polynomials for weighted sup-norm
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 10, pp. 1790-1795
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The behavior of the graph of the function $Z_n(t)=\|Z'_n(\cdot,t)\|/\|Z_n(\cdot,t)\|$ is discussed in the case where the functions $Z_n(x,t)$ are the Zolotarev polynomials and the norm is a weighted sup-norm. Based on calculations performed for various weights, it is conjectured that the characteristic jump in $Z_n(t)$ in the case of the Laguerre weight on a semiaxis is caused by the fact that the weight function is not symmetric about the midpoint of the interval.
@article{ZVMMF_2011_51_10_a3,
author = {V. P. Sklyarov},
title = {A~numerical experiment related to {Zolotarev} polynomials for weighted sup-norm},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1790--1795},
publisher = {mathdoc},
volume = {51},
number = {10},
year = {2011},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_10_a3/}
}
TY - JOUR AU - V. P. Sklyarov TI - A numerical experiment related to Zolotarev polynomials for weighted sup-norm JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2011 SP - 1790 EP - 1795 VL - 51 IS - 10 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_10_a3/ LA - ru ID - ZVMMF_2011_51_10_a3 ER -
%0 Journal Article %A V. P. Sklyarov %T A numerical experiment related to Zolotarev polynomials for weighted sup-norm %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2011 %P 1790-1795 %V 51 %N 10 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_10_a3/ %G ru %F ZVMMF_2011_51_10_a3
V. P. Sklyarov. A numerical experiment related to Zolotarev polynomials for weighted sup-norm. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 10, pp. 1790-1795. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_10_a3/