Mathematica 9 is now available Technology Guide--The Technology
Inside Matters Sparse Arrays  Sparse arrays are those in which
most of the elements (sparse matrices, or vectors, or tensors)
are zero or--more generally--a common value.  Mathematica's
SparseArray technology offers a uniquely efficient way to store
and manipulate large sparse objects of any dimension. Sparse
algorithms are automatically used where they would improve
performance, without user intervention, and can be manually
evoked. In fact, Mathematica can perform very-large-scale linear
algebra operations at higher speeds--and with smaller memory
footprints--than specialized numerical systems can.  Sparse
Arrays  Dramatic time savings can result from using sparse data
representation. The graph compares the time taken to solve
systems of linear equations utilizing sparse (red) and dense
(gray) representations. The effect becomes particularly
pronounced as the size of the calculation grows.  Note: Times
are for a 3.6 GHz Pentium 4 processor runn