Geodesic
On a weighted quasi-residual minimization strategy for solving complex symmetric shifted linear systems
Electronic transactions on numerical analysis, Tome 31 (2008), pp. 126-140
We consider the solution of complex symmetric shifted linear systems. Such systems arise in largescale electronic structure simulations, and there is a strong need of algorithms for their fast solution. With the aim of solving the systems efficiently, we consider a special case of the QMR method for non-Hermitian shifted linear systems and propose its weighted quasi-minimal residual approach. A numerical algorithm, referred to as shifted QMR $SYM(B)$, is obtained by the choice of a weight which is particularly cost-effective. Numerical examples are presented to show the performance of the shifted QMR $SYM(B)$ method.
Classification : 65F10
Keywords: complex symmetric matrices, shifted linear systems, Krylov methods, COCG, QMR SYM 
@article{ETNA_2008__31__a14,
     author = {Sogabe,  T. and Hoshi,  T. and Zhang,  S.-L. and Fujiwara,  T.},
     title = {On a weighted quasi-residual minimization strategy for solving complex symmetric shifted linear systems},
     journal = {Electronic transactions on numerical analysis},
     pages = {126--140},
     year = {2008},
     volume = {31},
     zbl = {1171.65023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__31__a14/}
}
TY  - JOUR
AU  - Sogabe,  T.
AU  - Hoshi,  T.
AU  - Zhang,  S.-L.
AU  - Fujiwara,  T.
TI  - On a weighted quasi-residual minimization strategy for solving complex symmetric shifted linear systems
JO  - Electronic transactions on numerical analysis
PY  - 2008
SP  - 126
EP  - 140
VL  - 31
UR  - http://geodesic.mathdoc.fr/item/ETNA_2008__31__a14/
LA  - en
ID  - ETNA_2008__31__a14
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%A Hoshi,  T.
%A Zhang,  S.-L.
%A Fujiwara,  T.
%T On a weighted quasi-residual minimization strategy for solving complex symmetric shifted linear systems
%J Electronic transactions on numerical analysis
%D 2008
%P 126-140
%V 31
%U http://geodesic.mathdoc.fr/item/ETNA_2008__31__a14/
%G en
%F ETNA_2008__31__a14
Sogabe,  T.; Hoshi,  T.; Zhang,  S.-L.; Fujiwara,  T. On a weighted quasi-residual minimization strategy for solving complex symmetric shifted linear systems. Electronic transactions on numerical analysis, Tome 31 (2008), pp. 126-140. http://geodesic.mathdoc.fr/item/ETNA_2008__31__a14/