Interval Valued Variational Analysis Using the Arithmetic of Higher Order Polynomial

In this paper, we discuss the two extensions of Affine Arithmetic, one through using higher order polynomial approximations, and the other is through partitioning the tolerance intervals. The two techniques greatly decrease the excessive width of calculated interval so that we could use these techniques to check the bounds in various kinds of circumstances such as variational timing analysis or circuit simulation. The accuracy of the simulation using this model is enhanced comparing with those using purely affine model.