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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 22, Iss. 22 — Nov. 15, 1983
  • pp: 3572–3578

Direct and implicit optical matrix–vector algorithms

David Casasent and Anjan Ghosh  »View Author Affiliations


Applied Optics, Vol. 22, Issue 22, pp. 3572-3578 (1983)
http://dx.doi.org/10.1364/AO.22.003572


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Abstract

New direct and implicit algorithms for optical matrix–vector and systolic array processors are considered. Direct rather than indirect algorithms to solve linear systems and implicit rather than explicit solutions to solve second-order partial differential equations are discussed. In many cases, such approaches more properly utilize the advantageous features of optical systolic array processors. The matrix-decomposition operation (rather than solution of the simplified matrix–vector equation that results) is recognized as the computationally burdensome aspect of such problems that should be computed on an optical system. The Householder QR matrix-decomposition algorithm is considered as a specific example of a direct solution. Extensions to eigenvalue computation and formation of matrices of special structure are also noted.

© 1983 Optical Society of America

History
Original Manuscript: May 4, 1983
Published: November 15, 1983

Citation
David Casasent and Anjan Ghosh, "Direct and implicit optical matrix–vector algorithms," Appl. Opt. 22, 3572-3578 (1983)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-22-22-3572


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References

  1. A. Edison, M. Noble, “Optical Analog Matrix Processors,” AD646060 (Nov.1966).
  2. P. Mengert et al., U.S. Patent3,525,856 (6Oct.1966).
  3. M. A. Monahan et al., Proc. IEEE 65, 121 (Jan.1977). [CrossRef]
  4. J. Goodman et al., Opt. Lett. 2, 1 (1978). [CrossRef] [PubMed]
  5. D. Psaltis et al., Opt. Lett. 4, 348 (1979). [CrossRef] [PubMed]
  6. M. Carlotto, D. Casasent, Appl. Opt. 21, 147 (1982). [CrossRef] [PubMed]
  7. H. J. Caulfield et al., Opt. Commun. 40, 86 (1981). [CrossRef]
  8. D. Casasent, Appl. Opt. 21, 1859 (1982). [CrossRef] [PubMed]
  9. D. Casasent, J. Jackson, C. Newman, Appl. Opt. 22, 115 (1983). [CrossRef] [PubMed]
  10. L. Richardson, Philos. Trans. R. Soc. London Ser. A, 210, 307 (1910).
  11. R. K. Montoye, D. H. Lawrie, IEEE Trans. Comput. C-31, 1076 (1982). [CrossRef]
  12. J. H. Wilkinson, The Algebraic Eigenvalue Problem (Clarendon, Oxford, 1965).
  13. E. Issacson, H. B. Keller, Analysis of Numerical Methods (Wiley, New York, 1966).
  14. A. R. Gourlay, G. A. Watson, Computational Methods for Matrix Eigenproblems (Wiley, London, 1973).
  15. J. Stoer, R. Bulirsch, Introduction to Numerical Analysis (Springer, New York, 1980).
  16. H. J. Caulfield, D. Dvore, J. W. Goodman, W. Rhodes, Appl. Opt. 20, 2263 (1981). [CrossRef] [PubMed]
  17. B. V. K. V. Kumar, D. Casasent, Appl. Opt. 20, 3707 (1981). [CrossRef] [PubMed]
  18. C. VanLoan, Math. Prog. Study 18, 102 (May1982). [CrossRef]
  19. L. Meirovitch, Computational Methods in Structural Dynamics (Sijthoff and Noordhoff International Publishers B.V., Alpehn aan den Rijn, The Netherlands, 1980).

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