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
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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.
@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
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/