of the resulting algorithm, referred to as shifted QMR\_SYM($B$), when the number of shifted linear systems is large enough.

The present paper is organized as follows: in the next section, shifted QMR\_SYM is described in order to specify the most time consuming part for a large number of shifted linear systems. In Section 3, we propose a WQMR approach with a specific weight for reducing the cost of the most time consuming part. The resulting algorithm, shifted QMR\_SYM($B$), and its properties are given. In Section 4, some results of numerical examples from electronic structure simulations are shown to see the performance of the shifted QMR\_SYM($B$) method. Finally, some concluding remarks are made in Section 5.

Throughout this paper, unless otherwise stated, all vectors and matrices are assumed to be complex. $\overline{M}$, $M^{\textrm{\scriptsize{T}}}$, $M^{\textrm{\scriptsize{H}}}=\overline{M}^{\textrm{\scriptsize{T}}}$ denote the complex conjugate, transpose, and Hermitian transpose matrix of the matrix $M$. $\|{\mbox{\boldmath $v$}}\|_W$ denotes the $W$-norm written as $({\mbox{\boldmath $v$}}^{\textrm{\scriptsize{H}}}W {\mbox{\boldmath $v$}})^{1/2}$, where $W$ is Hermitian positive definite.

The QMR\_SYM method for solving complex symmetric shifted linear systems
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In this section, the shifted QMR\_SYM method and its properties for solving complex symmetric shifted linear systems are introduced.

The QMR method for shifted linear systems 