.. _method-bayes_calibration-queso-emulator-mf_sc-piecewise:

"""""""""
piecewise
"""""""""


Use piecewise local basis functions


.. toctree::
   :hidden:
   :maxdepth: 1



**Specification**

- *Alias:* None

- *Arguments:* None

- *Default:* extended (Askey + numerically-generated)


**Description**


SC also supports the option of piecewise local basis functions. These are piecewise linear splines, or in the case of gradient-enhanced 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 high-order 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 Newton-Cotes points are employed in this case, and all random variable types are transformed to standard uniform probability space.


