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Dramatic time savings can result from using sparse data
representation. The graph compares the time taken to solve systems of
linear equations utilizing sparse (orange) 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 running Windows XP.
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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. In fact, Mathematica can perform very-large-scale
linear algebra operations at higher speeds--and with smaller memory
footprints--than specialized numerical systems can.
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