Sparsity-Directe d DecompositionforGaussian
John Walker · 1970
This isaconcise critical survey ofthetheory andprac- tice relating totheordered Gaussian elimination onsparse systems. Anewmethodofrenumbering byclusters isdeveloped, andits prop- erties described. Byestablishing acorrespondence between matrix pattems anddirected graphs, asequential binary partition isusedto decompose thenodesofagraphinto clusters. Byappropriate order- ingofthenodeswithin eachcluster andbyselecting clusters, oneat atime, bothoptimal ordering andauseful formofmatrix banding are achieved. Someresults pertaining tothecompatibility between optimal ordering forsparsity andtheusualpivoting fornumerical accuracy areincluded.