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Application of multigrid solvers in shifted linear systems is studied. Wefocus on accelerating the rational approximation needed for simulating singleflavor operators. This is particularly useful, in the case of twisted massfermions for mass non-degenerate quarks and can be employed to accelerate the$N_f=1+1$ sector of $N_f=2+1+1$ twisted mass fermion simulations. The multigridsolver is accelerated by employing suitable initial guesses. We propose a novelstrategy for proposing initial guesses for shifted linear systems based on theLagrangian interpolation of the previous solutions.

Multigrid approach in shifted linear systems for the non-degenerated twisted mass operator