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Local regression is a nonparametric method in which the regression surface is estimated by fitting parametric functions locally in the space of the predictors using weighted least squares in a moving fashion similar to the way that a time series is smoothed by moving averages. Three computational methods for local regression are presented. First, fast surface fitting and evaluation is achieved by building a k-d tree in the space of the predictors, evaluating the surface at the corners of the tree, and then interpolating elsewhere by blending functions. Second, surfaces are made conditionally parametric in any proper subset of the predictors by a simple alteration of the weighting scheme. Third, degree-of-freedom quantities that would be extremely expensive to compute exactly are approximated, not by numerical methods, but through a statistical model that predicts the quantities from the trace of the hat matrix, which can be computed easily.

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In this paper, we present an overview of the physical prin ciples and numerical methods used to solve the coupled system of non linear partial differential equations that model the transient behavior of silicon VLSI device structures. We also describe how the same tech