SPARSE GRIDS FOR ANISOTROPIC PROBLEMS

The classical sparse grid algorithm is often constructed
from a sequence of Clenshaw-Curtis rulesof exponentially
increasing order.  A set of sparse grids is produced, with
an index called the ``level''.  The grids are isotropic,
treating each dimension the same.  Each time the level
is incremented, the precision of the grid is increased 
in every dimension.  

We consider modifications of the classical algorithm which
allow each dimension to have a distinct geometry, weight
function, and quadrature rule.  Moreover, the user may
assign an importance to each dimension, so that some dimensions
are more thoroughly gridded than others.

Much of this presentation will involve the display of accuracy
plots showing which monomials a sparse grid can integrate exactly.
This suggests an adaptive approach, in which we consider 
adding ``nearby'' monomials to the current accuracy plot
to improve the results.