Sparse Matrix

A sparse matrix is a matrix that allows special techniques to take advantage of the large number of "background" (commonly zero) elements.

The number of zeros a matrix needs in order to be considered "sparse" depends on the structure of the matrix and the desired operations to perform on it. For example, a randomly generated sparse n×n matrix with cn entries scattered randomly throughout the matrix is not sparse in the sense of Wilkinson (for direct methods) since it takes O(n^3) time to factor (with high probability and for large enough c; Gilbert et al. 1992).

Portions of this entry contributed by Tim Davis

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Gilbert, J. R; Moler, C.; and Schreiber, R. "Sparse Matrices in MATLAB: Design and Implementation." SIAM J. Matrix Anal. Appl. 13, 333-356, 1992.Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. "Sparse Linear Systems." §2.7 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 63-82, 1992.

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Sparse Matrix

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Davis, Tim and Weisstein, Eric W. "Sparse Matrix." From MathWorld--A Wolfram Web Resource.

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