are generated for $\ell=1,2,\ldots,m$. On the other hand, if we apply the COCG method to just one of the shifted linear systems (\[CS\_SLS\]) (referred to as the “$seed\ system$”), then the Krylov basis vectors are generated from the seed system and these vectors are used to solve the rest of the shifted linear systems.

Based on the observation (\[KS\]), the shifted COCG method [@Shifted_COCG] has been recently proposed for solving complex symmetric shifted linear systems. The feature of the shifted COCG method is that the method performs COCG on a seed system and makes it possible to complete COCG for all shifted linear systems without further matrix-vector multiplications. The feature is completely different from some of the other well-known shifted linear solvers such as the shifted BiCGStab($\ell$) method [@Shifted_BiCGSSTABL] or the restarted shifted GMRES method [@Shifted_GMRES] since these perform BiCGStab($\ell$) (or GMRES) on a seed system but a different method on the shifted linear systems in order to keep the residuals colinear. The feature of the shifted COCG method plays a very important role in the seed switching technique [@Seed_switch] that avoids a minor problem of the shifted COCG method: one requires the choice of a seed system and an 