Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 12, pp. 2083-2091
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L. F. Yukhno. A stopping criterion for the iterative solution of an overdetermined system of linear algebraic equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 12, pp. 2083-2091. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_12_a0/
@article{ZVMMF_2008_48_12_a0,
author = {L. F. Yukhno},
title = {A~stopping criterion for the iterative solution of an overdetermined system of linear algebraic equations},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {2083--2091},
year = {2008},
volume = {48},
number = {12},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_12_a0/}
}
TY - JOUR
AU - L. F. Yukhno
TI - A stopping criterion for the iterative solution of an overdetermined system of linear algebraic equations
JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY - 2008
SP - 2083
EP - 2091
VL - 48
IS - 12
UR - http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_12_a0/
LA - ru
ID - ZVMMF_2008_48_12_a0
ER -
%0 Journal Article
%A L. F. Yukhno
%T A stopping criterion for the iterative solution of an overdetermined system of linear algebraic equations
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2008
%P 2083-2091
%V 48
%N 12
%U http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_12_a0/
%G ru
%F ZVMMF_2008_48_12_a0
For an overdetermined system of linear algebraic equations, systems obtained by introducing independent random errors into the original right-hand side are examined. Under certain assumptions on how these random variables are distributed, a practical stopping criterion is proposed for an iterative process that minimizes the sum of the squares of the residuals for the above systems. Numerical results demonstrating the efficiency of this criterion for some ill-conditioned problems are presented.
