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A combined unifrontal/multifrontal method for unsymmetric sparse matrices. (English) Zbl 0819.65029

Lewis, John G. (ed.), Applied linear algebra. Proceedings of the 5th SIAM conference, held in Snowbird, UT, USA, June 15-18, 1994. Philadelphia, PA: SIAM. 413-417 (1994).
Summary: In the multifrontal method, each frontal matrix much hold all of its pivot rows and columns at one time. Moving data between frontal matrices is costly, but the method can handle arbitrary fill-reducing orderings. In the unifrontal method, pivot rows and columns are shifted out of the frontal matrix as the factorization proceeds. Data movement is simpler, but higher fill-in can result.
We consider a hybrid unifrontal/multifrontal algorithm. Fill-reducing orderings can still be applied, but data movement is reduced by allowing pivot rows and columns to be shifted into and out of each frontal matrix (just as in the unifrontal method). Performance results on a Cray YMP supercomputer are presented.
For the entire collection see [Zbl 0809.00014].

MSC:

65F05 Direct numerical methods for linear systems and matrix inversion
65Y20 Complexity and performance of numerical algorithms
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