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Least-squares iterative solution on a fixed-size VLSI architecture

  • Session 9B: Algorithms, Architectures And Performance II
  • Conference paper
  • First Online:
Supercomputing (ICS 1987)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 297))

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Abstract

The VLSI implementation of the Accelerated Overrelaxation (AOR) method, when used for the accurate computation of the least-squares solutions of overdetermined systems, is the problem addressed here. As the size of this computational task is usually very large, we use space-time domain expansion techniques to partition the computation and map it onto a fixed size VLSI architecture.

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References

  1. J.H. Argyris and O.E. Brönlund, "The natural factor formulation of the stiffness matrix displacement method", Comput. Meth. Appl. Mech. Engrg. 5: 97–119, 1975.

    Google Scholar 

  2. J.H. Argyris, T.L. Johnson and H.P. Mlejnek, "On the natural factor in nonlinear analysis", Ibib. 15: 389–406, 1978.

    Google Scholar 

  3. S.C. Chen, D.J. Kuck and A.H. Sameh, "Practical Parallel Band Triangular System Solvers", ACM Trans. Math. Software, Vol. 4, No. 3, pp. 270–277, Sept. 1978.

    Google Scholar 

  4. Y.T. Chen, "Iterative methods for linear least-squares problems", Ph.D. Dissertation, Univ. of Waterloo, Canada, 1975.

    Google Scholar 

  5. H.D. Cheng and K.S. Fu, "Algorithm partition and parallel recognition of general context free languages using fixed size VLSI architecture", June 1984, Purdue University.

    Google Scholar 

  6. H.D. Cheng and K.S. Fu, "VLSI architectures for pattern matching using space-time domain expansion approach", October 1984, Purdue University.

    Google Scholar 

  7. H.D. Cheng and K.S. Fu, "Algorithm partition for a fixed size VLSI architecture using space-time domain expansion", Proc. 7th Symp. Comput. Arithmetic, June 1985, pp. 126–132.

    Google Scholar 

  8. H.D. Cheng, W.C. Lin and K.S. Fu, "Space-time domain expansion approach to VLSI and its application to hierarchical scene matching", IEEE Trans. on Pattern Anal. Mach. Int., March 1985.

    Google Scholar 

  9. G.H. Golub and R.J. Plemmons, "Large scale geothetic least squares adjustments by dissection and orthogonal decomposition", Linear Algebra and Appl., 34: 3–28, 1980.

    Google Scholar 

  10. A. Hadjidimos, "Accelerated Overrelaxation Method", Math. Comp. 32: 149–157, 1978.

    Google Scholar 

  11. K. Hwang and Y.H. Cheng, "Partitioned algorithms and VLSI structures for large-scale matrix computations", Proc. 5th Symp. Comput. Arithmetic, May 1981, pp. 222–232.

    Google Scholar 

  12. K. Hwang and Y.H. Chen, "Partitioned Matrix Algorithms for VLSI Arithmetic Systems", IEEE Trans, Comp., C-31 (12): 1215–1224, 1982.

    Google Scholar 

  13. I. Kaneco, M. Lawo and Thieraut, "On computational procedures for the force method", Intern. J. Num. Meth. Eng. 18: 1469–1495, 1982

    Google Scholar 

  14. C.B. Kolata, "Geodecy: dealing with an enormous computer task", Science, 200: 421–422, 1978.

    Google Scholar 

  15. D.I. Moldovan and J.A.B. Fortes, "Partitioning and Mapping Algorithms into fixed size systolic arrays", IEEE Trans. on Comp., C-35(1): 1–12, 1986.

    Google Scholar 

  16. D.I. Moldovan, C.I. Wu and J.A.B. Fortes, "Mapping an arbitrarily large QR algorithm into a fixed size VLSI array", Proc. of 1984 Int. Conf. on Parallel Processing, August 1984.

    Google Scholar 

  17. E.P. Papadopoulou, "VLSI structures and iterative analysis for large scale computation", Ph.D. Thesis, Clarkson University, 1986

    Google Scholar 

  18. E.P. Papadopoulou, T.S. Papatheodorou and Y.G. Saridakis, "Block AOR Iterative Schemes for Large-Scale Least-Squares Problems", to appear.

    Google Scholar 

  19. R.J. Plemmons, "Adjustment by least squares in geodesy using block iterative methods for sparse matrices", ARO Rept. 79-3, Proc. 1979 Army Num. Anal. Comp. Conf., El Paso, 1974.

    Google Scholar 

  20. J.R. Rice, RHRVEC workshop on very large least squares problems and supercomputers, CSD-TR 464, Computer Science Dept., Purdue University, Purdue, Indiana, 1983.

    Google Scholar 

  21. A.H. Sameh and R.P. Brent, "Solving Triangular Systems on a Parallel Computer", SIAM J. Number. Anal., Vol. 14, No. 6, pp. 1101–1113, Dec. 1977.

    Google Scholar 

  22. D.M. Young, "Iterative Solution of Large Linear Systems", Academic Press, New York, 1971.

    Google Scholar 

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E. N. Houstis T. S. Papatheodorou C. D. Polychronopoulos

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© 1988 Springer-Verlag Berlin Heidelberg

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Papadopoulou, E.P., Papatheodorou, T.S. (1988). Least-squares iterative solution on a fixed-size VLSI architecture. In: Houstis, E.N., Papatheodorou, T.S., Polychronopoulos, C.D. (eds) Supercomputing. ICS 1987. Lecture Notes in Computer Science, vol 297. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18991-2_53

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  • DOI: https://doi.org/10.1007/3-540-18991-2_53

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18991-6

  • Online ISBN: 978-3-540-38888-3

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