| Abstract: | Collocation has become a standard tool for approximation of parameterized
systems in the uncertainty quantification (UQ) community. Techniques for least-squares
regularization, compressive sampling recovery, and interpolatory reconstruction
are becoming standard tools used in a variety of applications. Selection of a collocation
mesh is frequently a challenge, but methods that construct geometrically unstructured
collocation meshes have shown great potential due to attractive theoretical
properties and direct, simple generation and implementation. We investigate properties
of these meshes, presenting stability and accuracy results that can be used as
guides for generating stochastic collocation grids in multiple dimensions. |
