Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 11, pp. 1991-1999
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E. A. Nurminski. Convergence of the suitable affine subspace method for finding the least distance to a simplex. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 11, pp. 1991-1999. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_11_a7/
@article{ZVMMF_2005_45_11_a7,
author = {E. A. Nurminski},
title = {Convergence of the suitable affine subspace method for finding the least distance to a simplex},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1991--1999},
year = {2005},
volume = {45},
number = {11},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_11_a7/}
}
TY - JOUR
AU - E. A. Nurminski
TI - Convergence of the suitable affine subspace method for finding the least distance to a simplex
JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY - 2005
SP - 1991
EP - 1999
VL - 45
IS - 11
UR - http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_11_a7/
LA - ru
ID - ZVMMF_2005_45_11_a7
ER -
%0 Journal Article
%A E. A. Nurminski
%T Convergence of the suitable affine subspace method for finding the least distance to a simplex
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2005
%P 1991-1999
%V 45
%N 11
%U http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_11_a7/
%G ru
%F ZVMMF_2005_45_11_a7
A minimum-length vector is found for a simplex in a finite-dimensional Euclidean space. The algorithm of successive projections onto affine subspaces containing suitable subsimplices of the initial simplex is shown to have a globally higher-than-linear convergence rate. Results of numerical experiments are presented.
[1] Bauschke H. H., Borwein J. M., “On projection algorithms for solving convex feasibility problems”, SIAM Revs., 38:3 (1996), 367–426 | DOI | MR | Zbl
[2] Nurminskii E. A., “Parallelnyi metod proektsii na vypukluyu obolochku semeistva mnozhestv”, Izv. vuzov. Matematika, 12:499 (2003), 78–82 | MR | Zbl
[3] Nurminskii E. A., “Metod posledovatelnykh proektsii dlya resheniya zadachi o naimenshem rasstoyanii dlya simpleksov”, Elektronnyi zhurnal “Issledovano v Rossii”, 160 (2004), 1732–1739 http://zhurnal.ape.relarn.rn/articles/2004/160.pdf
[4] Bregman L. M., “Nakhozhdenie obschei tochki vypuklykh mnozhestv metodom posledovatelnogo proektirovaniya”, Dokl. AN SSSR, 162:3 (1965), 487–490 | MR | Zbl
[5] Gurin L. G., Polyak B. T., Raik E. V., “Metody proektsii dlya otyskaniya obschei tochki vypuklykh mnozhestv”, Zh. vychisl. matem. i matem. fiz., 7 (1967), 1211–1228 | MR
[6] Demyanov V. F., Malozemov V. N., Vvedenie v minimaks, Nauka, M., 1972 | MR
