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Modified Faddeeva Algorithm for Concurrent Execution of Linear Algebraic Operations
February 1988 (vol. 37 no. 2)
pp. 129-137
An algorithm is described that provides an architectural framework for systematic execution of a wide class of linear algebraic operations using a single systolic array and simple data flow. The algorithm has been modified to use numerically stable Given's rotations and is therefore suited to any matrix problem of full rank. When the problem size exceeds that of the hardware array, it can be pa

[1] H. T. Kung, "On the implementation and use of systolic array processors," inProc. 1983 IEEE Int. Conf. Comput. Design, Port Chester, NY, pp. 370-373.
[2] J. G. Nash, "VLSI implementation of a linear systolic array," inProc. 1985 Int. Conf. Acoust., Speech, Signal Processing, Tampa, FL, pp. 1392-1395.
[3] S. J. Leon,Linear Algebra with Applications. New York: MacMillan, 1980.
[4] J. Allen, "Computer architecture for digital signal processing,"Proc. IEEE, pp. 852-873, May 1985.
[5] J. M. Speiser and H. J. Whitehouse, "Architectures for real-time matrix operations," inProc. 1980 Government Microcircuit Appl. Conf., Houston, TX, Nov. 19-21, 1980.
[6] H. C. Andrews and B. R. Hunt,Digital Image Restoration. Englewood Cliffs, NJ: Prentice-Hall, 1977.
[7] J. Fisher, "The MPP at Goddard-Three years of use," inProc. Comput. Architecture Pattern Anal. Image Data Base Management Workshop, Miami Beach, FL, Nov. 18-20, 1985.
[8] J. G. Nash and S. Hansen, "Modified Faddeeva algorithm for matrix manipulation," inProc. 1984 SPIE Conf., San Diego, CA, Aug. 1984.
[9] V. N. Faddeeva,Computational Methods of Linear Algebra. Dover, 1959, translated by C. D. Benster.
[10] R. W. Cottle, "Manifestations of the Schur complement,"Linear Algebra and its Applications, vol. 8, pp. 189-211, 1974.
[11] J. G. Nash, S. Hansen, and G. R. Nudd "VLSI processor arrays for matrix manipulation," inVLSI Systems and Computations, H. T. Kung, B. Sproull and G. Steel, Eds. Rockville, MD: Computer Science Press, 1981, pp. 367-378.
[12] H. T. Kung, "Systolic array for orthogonal triangularization," inProc. SPIE, San Diego, CA, 1981, pp. 19-26.
[13] G. H. Golub and C. Van Loan,Matrix Computations. Baltimore, MD: Johns Hopkins University Press, 1983.
[14] C. C. Paige, "Computer solution and perturbation analysis of generalized least squares problems,"Math Computat., vol. 33, pp. 171-183, 1979.
[15] H. Y. H. Chuang and G. He, "A versatile systolic array for matrix computations," inProc. 12th Int. Conf. Comput. Architecture, Boston, MA, June 1985, pp. 315-322.
[16] F. Luk, "A triangular processor array for computing the singular value decomposition," Cornell Tech. Rep. TR 84-625, July 1984.
[17] J. G. Nash, W. Przytula, and S. Hansen, "Systolic partitioned and
[18] K. Wojtek Przytula, J. G. Nash, and S. Hansen, "FFT algorithm for 2- D array processors," inProc. SPIE, San Diego, CA, Aug. 1987.
[19] J. G. Nash, K. Wojtek Przytula, and S. Hansen, "The systolic/cellular system for signal processing,"Computer, pp. 96-97, July 1987.

Index Terms:
modified Faddeeva algorithm; full-rank matrix problems; numerically-stable partitioning; data flow architecture; concurrent execution; linear algebraic operations; systolic array; numerically stable Given's rotations; convergence of numerical methods; linear algebra; parallel algorithms; parallel architectures.
Citation:
J.G. Nash, S. Hansen, "Modified Faddeeva Algorithm for Concurrent Execution of Linear Algebraic Operations," IEEE Transactions on Computers, vol. 37, no. 2, pp. 129-137, Feb. 1988, doi:10.1109/12.2142
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