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A Fast Faddeev Array
December 1992 (vol. 41 no. 12)
pp. 1594-1600

A systolic array for the fast computation of the Faddeev algorithm is presented. Inversion of an n*n matrix on a systolic array is known to tend to 5 n inner product steps under the assumption that no data are duplicated. The proposed Faddeev array achieves matrix inversion in just 4 n steps with O(n/sup 2/) basic cells using careful duplications of some data. The array consists of two half-arrays which compute two separate but coupled triangularizations. The coupling is resolved by an on-the-fly decoupling process which duplicates pivot row data and passes them between the arrays using only nearest neighbor connections.

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Index Terms:
data duplications; fast Faddeev array; systolic array; Faddeev algorithm; inner product steps; matrix inversion; half-arrays; triangularizations; on-the-fly decoupling; pivot row data; nearest neighbor connections; computational complexity; matrix algebra; parallel algorithms; systolic arrays.
G.M. Megson, "A Fast Faddeev Array," IEEE Transactions on Computers, vol. 41, no. 12, pp. 1594-1600, Dec. 1992, doi:10.1109/12.214668
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