  Matrix computations, especially iterative PDE solving (and the sparse matrix
vector multiplication subproblem within) using conjugate gradient algorithm,
and LU/Cholesky decomposition for solving system of linear equations, form the
kernel of many applications, such as circuit simulators, computational fluid
dynamics or structural analysis etc. The problem of designing approaches for
parallelizing these computations, to get good speedups as much as possible as
per Amdahl's law, has been continuously researched upon. In this paper, we
discuss approaches based on the use of finite projective geometry graphs for
these two problems. For the problem of conjugate gradient algorithm, the
approach looks at an alternative data distribution based on projective-geometry
concepts. It is proved that this data distribution is an optimal data
distribution for scheduling the main problem of dense matrix-vector
multiplication. For the problem of parallel LU/Cholesky decomposition of
general matrices, the approach is motivated by the recently published scheme
for interconnects of distributed systems, perfect difference networks. We find
that projective-geometry based graphs indeed offer an exciting way of
parallelizing these computations, and in fact many others. Moreover, their
applications ranges from architectural ones (interconnect choice) to
algorithmic ones (data distributions).
