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We consider the solution of complex symmetric shifted linear systems. Suchsystems arise in large-scale electronic structure simulations and there is astrong need for the fast solution of the systems. With the aim of solving thesystems efficiently, we consider a special case of the QMR method fornon-Hermitian shifted linear systems and propose its weighted quasi-minimalresidual approach. A numerical algorithm, referred to as shifted QMR\_SYM($B$),is given by the choice of a particularly cost-effective weight. Numericalexamples are presented to show the performance of the shifted QMR\_SYM($B$)method.

On a weighted quasi-residual minimization strategy of the QMR method for solving complex symmetric shifted linear systems