Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 12, pp. 2138-2148
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M. Dana; Kh. D. Ikramov. A numerical comparison of two minimal residual methods for linear polynomials in unitary matrices. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 12, pp. 2138-2148. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_12_a2/
@article{ZVMMF_2006_46_12_a2,
author = {M. Dana and Kh. D. Ikramov},
title = {A~numerical comparison of two minimal residual methods for linear polynomials in unitary matrices},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {2138--2148},
year = {2006},
volume = {46},
number = {12},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_12_a2/}
}
TY - JOUR
AU - M. Dana
AU - Kh. D. Ikramov
TI - A numerical comparison of two minimal residual methods for linear polynomials in unitary matrices
JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY - 2006
SP - 2138
EP - 2148
VL - 46
IS - 12
UR - http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_12_a2/
LA - ru
ID - ZVMMF_2006_46_12_a2
ER -
%0 Journal Article
%A M. Dana
%A Kh. D. Ikramov
%T A numerical comparison of two minimal residual methods for linear polynomials in unitary matrices
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2006
%P 2138-2148
%V 46
%N 12
%U http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_12_a2/
%G ru
%F ZVMMF_2006_46_12_a2
Two minimal residual methods for solving linear systems of the form $(\alpha U+\beta I)x=b$, where $U$ is a unitary matrix, are compared numerically. The first method uses conventional Krylov subspaces, while the second involves generalized Krylov subspaces. Experiments favor the second method if $|\alpha|>|\beta|$. Moreover, the greater the ratio $|\alpha|/|\beta|$, the higher the superiority of the second method.
