Exponential grids in high-dimensional space

Peter R. Brune; Matthew G. Knepley; L. Ridgway Scott. 15 December, 2011.
Communicated by L. Ridgway Scott.


We consider the approximation of functions that are localized in space. We show that it is possible to define meshes to approximate such functions with the property that the number of vertices grows only linearly in dimension. In one dimension, we discuss the optimal mesh for approximating exponentially decreasing functions. We review the use of Cartesian product grids in multiple dimensions introduced in a paper of Bank and Scott [4].

Original Document

The original document is available in PDF (uploaded 15 December, 2011 by L. Ridgway Scott).