On the properties of optimal point configurations for a family of comparison functionals for metric configurations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 9, pp. 1720-1727
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The problem of searching for an optimal point configuration (i.e., a set of points such that the distances between them best fit a given metric configuration) is considered. An upper bound is obtained for the dimension of a space in which any metric configuration can be represented exactly or approximately by an optimal point configuration. It is shown that, if there is no point configuration that exactly represents a given metric configuration, then, for a natural family of comparison functionals for metric configurations, the dimension of a space in which there is an optimal point configuration is lower than the dimension required in the general case for representing a metric configuration of a given cardinality.
@article{ZVMMF_2005_45_9_a14,
author = {A. I. Maysuradze},
title = {On the properties of optimal point configurations for a family of comparison functionals for metric configurations},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1720--1727},
publisher = {mathdoc},
volume = {45},
number = {9},
year = {2005},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_9_a14/}
}
TY - JOUR AU - A. I. Maysuradze TI - On the properties of optimal point configurations for a family of comparison functionals for metric configurations JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 2005 SP - 1720 EP - 1727 VL - 45 IS - 9 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_9_a14/ LA - ru ID - ZVMMF_2005_45_9_a14 ER -
%0 Journal Article %A A. I. Maysuradze %T On the properties of optimal point configurations for a family of comparison functionals for metric configurations %J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki %D 2005 %P 1720-1727 %V 45 %N 9 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_9_a14/ %G ru %F ZVMMF_2005_45_9_a14
A. I. Maysuradze. On the properties of optimal point configurations for a family of comparison functionals for metric configurations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 9, pp. 1720-1727. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_9_a14/