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| G.M. Megson, "A Fast Faddeev Array," IEEE Transactions on Computers, vol. 41, no. 12, pp. 1594-1600, December, 1992. | |||
| BibTex | x | ||
| @article{ 10.1109/12.214668, author = {G.M. Megson}, title = {A Fast Faddeev Array}, journal ={IEEE Transactions on Computers}, volume = {41}, number = {12}, issn = {0018-9340}, year = {1992}, pages = {1594-1600}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.214668}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Computers TI - A Fast Faddeev Array IS - 12 SN - 0018-9340 SP1594 EP1600 EPD - 1594-1600 A1 - G.M. Megson, PY - 1992 KW - 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. VL - 41 JA - IEEE Transactions on Computers ER - | |||
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.
[1] Y. Robert and D. Trystram, "Systolic solution of the algebraic path problem," inSystolic Arrays, W. Mooreet. al., Eds. Bristol, England: Adam Hilger, 1987, pp. 171-180.
[2] S. Y. Kung, S. C. Lo, and P. S. Lewis, "Optimal systolic design for the transitive closure problem,"IEEE Trans. Comput., vol. C-36, no. 5, pp. 603-614, May 1987.
[3] J. G. Nash and S. Hansen, "Modified Faddeev algorithm for matrix manipulation," inProc. 1984 SPIE Conf., San Diego, CA, Aug. 1984.
[4] Y. Robert and M. Tchuente, "Resolution Systolique de systemes linearies denses,"RAIRO modelisation et Analyse, Numerique 19, pp. 315-326, 1985.
[5] A. El-Amawy, "A systolic architecture for fast dense matrix inversion,"IEEE Trans. Comput.vol. C-38, no. 3, pp. 449-455, 1989.
[6] S. Y. Kung, "On supercomputing with systolic wavefront array processors,"IEEE Proc.vol. 72, pp. 867-884, 1984.
[7] H. T. Kung and C. E. Leiserson, "Systolic array (for VLSI)," inSparse Matrix Proc. 1978, SIAM, 1979, pp. 256-282.
[8] V. N. Faddeev,Computational Methods of Linear Algebra. New York: Dover, 1959.
[9] W. M. Gentleman and H. T. Kung, "Matrix triangularisation by systolic arrays,"SPIE Real-Time Signal Processing IV, 298 1981, pp. 19-26.
[10] K. Jainawdunsing and E. F. Deprettere, "A new class for parallel algorithms for solving linear equations,"SIAM J. Sci. Stat. Comput., vol. 10, no. 5, pp. 880-912, Sept. 1989.
[11] G. A. Rote, "Systolic array for the Algebraic path problem (shortest paths; matrix inversion),"Computing, vol. 34, pp. 191-219, 1985.
[12] G. M. Megson and F. M. F. Gaston, "Improved matrix triangularisation using a double pipeline systolic array,"Inform. Processing Lett., vol. 36, 1990.