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Year 2

Extend our work on geometric objects to arbitrary dimension.
(There are immediate scientific applications for threedimensional
representations, but we would prefer to solve the general problem
during Year 2.) High dimensional geometric objects require careful
thinking about representation formats, because converting from one
format to another often requires resources superexponential in the
dimension.

Generation of parallel code for sparse matrix applications.
We will generate parallel implementations of sparse iterative solvers
(such as conjugate gradient method), starting from dense, sequential
solvers. This will use restructuring compiler technology we have
developed at Cornell, as well as program transformation technology
which will be developed under the aegis of this grant.

Extend the MathBus specifications to deal with directed and
undirected graphs. The basis for much of sparse matrix computation is
graph theory. For instance, a preprocessing step of many sparse
matrix algorithms is called ``symbolic factorization'' and involves
some elegant graph algorithms [42]. A key to high
performance sparse matrix algorithms is identifying certain cliques in
the elimination order [72]. We will define a specification for
directed and undirected graphs in the mathematical bus.
 Extend the scope of the mathematical bus to include other
software packages such as LAPACK, visualization tools, Matlab, and
Maple.
nuprl project
Tue Nov 21 08:50:14 EST 1995