Polynomial Approximation on a Sparse Grid
We study polynomial approximation on a certain class of sparse grids that we call quasi-uniform. Using Boolean sum techniques combined with a Bernstein class of dual bases in subspaces, we construct quasi interpolants on these grids. Our construction achieves rates of approximation analogous to those on a tensor product grid, while retaining some geometric properties of Bernstein-Bezier surfaces.
International Conference on Approximation Theory (AT)
San Antonio, TX
Kersey, Scott N..
"Polynomial Approximation on a Sparse Grid."
Mathematical Sciences Faculty Presentations.