## Predicting Structure In Sparse Matrix Computations (1994)

Venue: | SIAM J. Matrix Anal. Appl |

Citations: | 40 - 4 self |

### BibTeX

@ARTICLE{Gilbert94predictingstructure,

author = {John R. Gilbert},

title = {Predicting Structure In Sparse Matrix Computations},

journal = {SIAM J. Matrix Anal. Appl},

year = {1994},

volume = {15},

pages = {62--79}

}

### Years of Citing Articles

### OpenURL

### Abstract

. Many sparse matrix algorithms---for example, solving a sparse system of linear equations---begin by predicting the nonzero structure of the output of a matrix computation from the nonzero structure of its input. This paper is a catalog of ways to predict nonzero structure. It contains known results for problems including various matrix factorizations, and new results for problems including some eigenvector computations. Key words. sparse matrix algorithms, graph theory, matrix factorization, systems of linear equations, eigenvectors AMS(MOS) subject classifications. 15A18, 15A23, 65F50, 68R10 1. Introduction. A sparse matrix algorithm is an algorithm that performs a matrix computation in such a way as to take advantage of the zero/nonzero structure of the matrices involved. Usually this means not explicitly storing or manipulating some or all of the zero elements; sometimes sparsity can also be exploited to work on different parts of a matrix problem in parallel. Large sparse matr...