Sparsity-Directed Decomposition for Gaussian Elimination on Matrices

@inproceedings{OGBUOBIRI2009SparsityDirectedDF,
  title={Sparsity-Directed Decomposition for Gaussian Elimination on Matrices},
  author={E. C. OGBUOBIRI and William F. Tinney and Senior Member and John Withers Walker},
  year={2009}
}
This is a concise critical survey of the theory and practice relating to the ordered Gaussian elimination on sparse systems. A new method of renumbering by clusters is developed, and its properties described. By establishing a correspondence between matrix pattems and directed graphs, a sequential binary partition is used to decompose the nodes of a graph into clusters. By appropriate ordering of the nodes within each cluster and by selecting clusters, one at a time, both optimal ordering and a… CONTINUE READING

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