Excited State Effects in Nucleon Matrix Element Calculations

We perform a high-statistics precision calculation of nucleon matrix elements using an open sink method allowing us to explore a wide range of sink-source time separations. In this way the influence of excited states of nucleon matrix elements can be studied. As particular examples we present results for the nucleon axial charge $g_A$ and for the first moment of the isovector unpolarized parton distribution $<x>_{u-d}$. In addition, we report on preliminary results using the generalized eigenvalue method for nucleon matrix elements. All calculations are performed using $N_f=2+1+1$ maximally twisted mass Wilson fermions.