Numerical Differentiation Using Statistical Design

Abstract

Derivatives are frequently required by numerical procedures across many disciplines. Numerical differentiation can be useful for approximating derivatives. This dissertation will introduce computational differentiation (the process by which derivatives are obtained with a computer), focusing on statistical response surface (RSM) designs for approximating derivatives. The RSM designs are compared with two competing numerical methods: namely a rival saturated statistical design approach, and a method employing finite differencing. A covariance model incorporating function curvature and computer round-off error is proposed for estimating the derivative approximation variances. These variances and the computational workload each method requires become the basis for comparing the derivative approximations. A diagnostic test for variable scaling errors is also described.