  In this paper, we study the accuracy of Irving-Kirkwood type of formulas for
the approximation of continuum quantities from atomistic simulations. Such
formulas are derived by expressing the displacement, deformation gradient and
stress in terms of certain kernel functions. We propose two criteria for
choosing the kernel functions to significantly improve the sampling accuracy.
We present a simple procedure to construct kernel functions that meet these
criteria. Further, numerical tests on homogeneous and non-homogeneous systems
provide validations for our analysis.
