  This study is mainly focused on iterative solutions to shifted linear systems
arising from a Quantum Chromodynamics (QCD) problem. To solve such system
efficiently, we explore a kind of shifted QMRCGstab (SQMRCGstab) methods, which
is derived by extending the quasi-minimum residual to the shifted BiCGstab. The
shifted QMRCGstab method takes advantage of the shifted structure, so that the
number of matrix-vector products and the number of inner products are the same
as a single linear system. Moreover, the SQMRCGstab achieves a smoothing of the
residual compared to the shifted BiCGstab, and is more competitive than the
MS-QMRIDR(s) and the shifted BiCGstab on the QCD problem. Numerical examples
show also the efficiency of the method when one applies it to the real
problems.
