  We consider a quadrature-based eigensolver to find eigenpairs of Hermitian
matrices arising in lattice quantum chromodynamics. To reduce the computational
cost for finding eigenpairs of such Hermitian matrices, we propose a new
technique for solving shifted linear systems with complex shifts by means of
the shifted CG method. Furthermore using integration paths along horizontal
lines corresponding to the real axis of the complex plane, the number of
iterations for the shifted CG method is also reduced. Some numerical
experiments illustrate the accuracy and efficiency of the proposed method by
comparison with a conventional method.
