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Mathematics of Computation

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On the number of nonzeros added when Gaussian elimination is performed on sparse random matrices


Author: I. S. Duff
Journal: Math. Comp. 28 (1974), 219-230
MSC: Primary 65F99
DOI: https://doi.org/10.1090/S0025-5718-1974-0331756-7
MathSciNet review: 0331756
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Abstract: This paper studies the fill-in properties of Gaussian elimination on sparse random matrices. A theoretical study using the concept of random graphs yields formulae from which the fill-in can be evaluated. The predictions are examined for matrices of various orders and densities and are found to be in close agreement with experimental results. A possible consequence of the results of this paper relating to error analysis for sparse systems is given in the concluding section.


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DOI: https://doi.org/10.1090/S0025-5718-1974-0331756-7
Keywords: Sparse random matrix, Gaussian elimination, fill-in, random graphs, legal paths, error analysis
Article copyright: © Copyright 1974 American Mathematical Society