Dakota Reference Manual
Version 6.4
LargeScale Engineering Optimization and Uncertainty Analysis

Use piecewise local basis functions
Alias: none
Argument(s): none
Default: extended (Askey + numericallygenerated)
SC also supports the option of piecewise local basis functions. These are piecewise linear splines, or in the case of gradientenhanced interpolation via the use_derivatives specification, piecewise cubic Hermite splines. Both of these basis selections provide local support only over the range from the interpolated point to its nearest 1D neighbors (within a tensor grid or within each of the tensor grids underlying a sparse grid), which exchanges the fast convergence of global bases for smooth functions for robustness in the representation of nonsmooth response functions (that can induce Gibbs oscillations when using highorder global basis functions). When local basis functions are used, the usage of nonequidistant collocation points (e.g., the Gauss point selections described above) is not well motivated, so equidistant NewtonCotes points are employed in this case, and all random variable types are transformed to standard uniform probability space.