Abstract
A fixed-size systolic array which can efficiently triangularize arbitrarily large matrices is presented. The array performs orthogonal triangularization by applying Givens' rotations in parallel. For matrices larger than the array, the triangularization is accomplished by emulating a large array with the fixed-size array. The distinguishing features of this array are (1) only one type of cell is used, (2) only unidirectional data flow is required, and (3) the array is rectangular shaped. These properties make it more suitable to emulate arbitrarily large arrays by feedback emulation.
The array can also efficiently compute the eigenvalues of arbitrarily large matrices by theQR algorithm, because it can also perform theQR decomposition. In the computation the rotation parameters generated during each stage of theQR decomposition are used in the multiplication before the next stage of decomposition.
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References
A. Jennings, inMatrix Computation for Engineers and Scientists, pp. 139–141. Wiley, New York, 1978.
J. H. Wilkinson,The Algebraic Eigenvalue Problem, pp. 515–520, Clarendon Press, Oxford, 1965.
H. T. Kung, Why Systolic Architectures?,Computer,15 (1), 37–45, 1982.
W. M. Gentleman and H. T. Kung, Matrix Triangularization by Systolic Arrays,Proc. SPIE Symposium on Real-time Signal Processing IV, pp. 19–26, 1981.
A. Bojanczyk, R. P. Brent, and H. T. Kung, Numerically Stable Solution of Dense Systems of Linear Equations Using Mesh-connected Processors,SIAM J. Sci. Statist. Comput.,5 (1), 95–104, 1984.
J. J. Navarro, J. M. LLaberia, and M. Valero, Solving Matrix Problems with No Size Restriction on a Systolic Array Processor,Proc. International Conference on Parallel Processing, pp. 676–683, 1986.
K. Hwang and Y. H. Cheng, Partitioned Algorithms and VLSI Structures for Large-scale Matrix Computations,Proc. IEEE Computer Society 5th Symposium on Computer Arithmetics, pp. 226–230, 1981.
H. D. Cheng and K. S. Fu, Algorithm Partition for Fixed-size VLSI Architecture Using Space-Time Domain Expansion,Proc. 7th Symposium on Computer Arithmetic, pp. 126–132, 1985.
D. Heller, Partitioning Big Matrices for Small Systolic Arrays,VLSI and Modern Signal Processing, pp. 185–199, Prentice-Hall, Englewood Cliffs, NJ, 1985.
P. A. Nelson and L. Snyder, Programming Solutions to the Algorithm Contraction Problem,Proc. International Conference on Parallel Processing, pp. 258–261, 1986.
H. Y. H. Chuang and G. He, A Versatile Systolic Array for Matrix Computations,Proc. International Symposium on Computer Architecture, pp. 315–322, 1985.
D. I. Moldovan, C. I. Wu, and J. A. B. Foates, Map** an Arbitrarily LargeQR Algorithm into a Fixed-Size VLSI Array,Proc. International Conference on Parallel Processing, pp. 365–373, 1984.
John P. Fishburn and R. A. Finkel, Quotient Networks,IEEE Trans. Comput.,31 (4), 288–295, 1982.
H. Y. H. Chuang and G. He, Design of Problem-size Independent Systolic Array Systems,Proc. International Conference on Computer Design: VLSI in Computers, pp. 152–157, 1984.
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Chuang, H.Y.H., Chen, L. & Qian, D. A size-independent systolic array for matrix triangularization and eigenvalue computation. Circuits Systems and Signal Process 7, 173–189 (1988). https://doi.org/10.1007/BF01602096
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DOI: https://doi.org/10.1007/BF01602096