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 running Windows XP.

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