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Sparse Gaussian elimination with controlled fill-in on a shared memory multiprocessor

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2 Author(s)
Alaghband, Gita ; Dept. of Electr. & Comput. Eng., Colorado Univ., Boulder, CO, USA ; Jordan, H.F.

It is shown that in sparse matrices arising from electronic circuits, it is possible to do computations on many diagonal elements simultaneously. A technique for obtaining an ordered compatible set directly from the ordered incompatible table is given. The ordering is based on the Markowitz number of the pivot candidates. This technique generates a set of compatible pivots with the property of generating few fills. A novel heuristic algorithm is presented that combines the idea of an order-compatible set with a limited binary tree search to generate several sets of compatible pivots in linear time. An elimination set for reducing the matrix is generated and selected on the basis of a minimum Markovitz sum number. The parallel pivoting technique presented is a stepwise algorithm and can be applied to any submatrix of the original matrix. Thus, it is not a preordering of the sparse matrix and is applied dynamically as the decomposition proceeds. Parameters are suggested to obtain a balance between parallelism and fill-ins. Results of applying the proposed algorithms on several large application matrices using the HEP multiprocessor are presented and analyzed

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Computers, IEEE Transactions on  (Volume:38 ,  Issue: 11 )