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.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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},
     publisher = {mathdoc},
     volume = {31},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2008__31__a14/}
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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/