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The Computer Journal 1967 10(3):300-305; doi:10.1093/comjnl/10.3.300
© 1967 by British Computer Society
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Row-column permutation of sparse matrices

R. P. Tewarson *

Department of Applied Analysis, State University of New York, Stony Brook, New York, USA

The problem of transforming a given sparse matrix A into a block diagonal form (b.d.f.) and the subsequent transformation of each of the block diagonal matrices into as nearly upper triangular form (u.t.f.) as possible, by using only row and column permutations, is discussed. It is shown how some of the results from Graph Theory can be used to transform A to the b.d.f. In order to transform the block diagonal matrices into the u.t.f.'s, two methods are described, one of which makes use of linear programming while the other uses approximate probabilistic arguments. The latter method, in relation to the computational effort, yields significant results in practice.


* Department of Applied Analysis, State University of New York, Stony Brook, N.Y. 11790, U.S.A. This research was supported in part by the National Aeronautics and Space Administration, Washington, D.C., Grant No. NGR–33–015–013.


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