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

We consider the solution of complex symmetric shifted linear systems. Such systems arise in large-scale electronic structure simulations and there is a strong need for the fast solution of the systems. 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 given by the choice of a particularly cost-effective weight. Numerical examples are presented to show the performance of the shifted QMR\_SYM($B$) method.