Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 11, pp. 1928-1937
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M. Dana; A. G. Zykov; Kh. D. Ikramov. A minimal residual method for a special class of linear systems with normal coefficients matrices. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 11, pp. 1928-1937. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_11_a2/
@article{ZVMMF_2005_45_11_a2,
author = {M. Dana and A. G. Zykov and Kh. D. Ikramov},
title = {A minimal residual method for a special class of linear systems with normal coefficients matrices},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1928--1937},
year = {2005},
volume = {45},
number = {11},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_11_a2/}
}
TY - JOUR
AU - M. Dana
AU - A. G. Zykov
AU - Kh. D. Ikramov
TI - A minimal residual method for a special class of linear systems with normal coefficients matrices
JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY - 2005
SP - 1928
EP - 1937
VL - 45
IS - 11
UR - http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_11_a2/
LA - ru
ID - ZVMMF_2005_45_11_a2
ER -
%0 Journal Article
%A M. Dana
%A A. G. Zykov
%A Kh. D. Ikramov
%T A minimal residual method for a special class of linear systems with normal coefficients matrices
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2005
%P 1928-1937
%V 45
%N 11
%U http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_11_a2/
%G ru
%F ZVMMF_2005_45_11_a2
A minimal residual method is constructed for the class of linear systems with normal coefficient matrices whose spectra belong to algebraic curves of a low order $k$. From the well-known GMRES algorithm, the proposed method differs by the choice of the subspaces in which approximate solutions are sought; as a consequence, the latter method is described by a short-term recurrence. The case $k=2$ is discussed at length. Numerical results are presented that confirm the significant superiority of the proposed method over the GMRES as applied to the linear systems specified above.
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