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abstract: '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.'
author:
- 'T. Sogabe[^1]'
- 'T. Hoshi[^2]'
- 'S.-L. Zhang$^\dagger$'
- 'T. Fujiwara[^3]'
title: 'On a weighted quasi-residual minimization strategy of the QMR method for solving complex symmetric shifted linear systems[^4]'
---

Introduction
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In this paper we consider the solution of complex symmetric shifted linear systems of the form $$\begin{aligned}
  (A+\sigma_\ell I){\mbox{\boldmath $x$}}^{(\ell)}={\mbox{\boldmath $b$}}, \quad   \ell=1,2,\ldots,m,  \label{CS_SLS}\end{aligned}$$ where $A({\sigma_\ell}):=A+\sigma_\ell I$ are nonsingular $N$-by-$N$ complex symmetric sparse matrices, i.e., $A(\sigma_\ell)=A(\sigma_\ell)^{\textrm{\scriptsize{T}}}\neq \overline{A}(\sigma_\ell)^{\textrm{\scriptsize{T}}}$, with scalar shifts $\sigma_\ell \in \mathbf{C}$, $I$ is the $N$-by-$N$ identity matrix, and ${\mbox{\boldmath $x$}}^{(\ell)}, {\mbox{\boldmath $b$}}$ are complex vectors of length $N$. The above systems arise in large-scale electronic structure simulations [@Shifted_COCG], and there is 