Abstract

A bidirection matrix–vector multiplication scheme leads to faster convergence as well as guaranteed convergence in a relaxation processor for parallel solution of linear algebraic equations when used in a bimodal optical computer.

© 1990 Optical Society of America

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References

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  1. H. J. Caulfield et al., “Bimodal Optical Computers,” Appl. Opt. 25, 3128–3131 (1986).
    [Crossref] [PubMed]
  2. M. A. G. Abushagur, H. John Caulfield, “Speed and Convergence of Bimodal Optical Computers,” Opt. Eng. 26, 022–027 (1987).
    [Crossref]
  3. M. A. G. Abushagur, “Adaptive Array Radar Data Processing Using the Bimodal Optical Computer,” Microwave Opt. Tech. Lett. 1, 236–240 (1988).
    [Crossref]
  4. M. A. G. Abushagur, H. John Caulfield, P. M. Gibson, M. A. Habli, “Superconvergence of Hybrid Optoelectronic Processors,” Appl. Opt. 26, 4906–4907 (1987).
    [Crossref] [PubMed]
  5. W. K. Cheng, H. J. Caulfield, “Fully Parallel Relaxation Algebraic Operations for Optical Computers,” Opt. Commun. 43, 251–254 (1982).
    [Crossref]
  6. V. Scholtz, E. Van Rooyen, Author: Insert Affiliation; private communication (1989).

1988 (1)

M. A. G. Abushagur, “Adaptive Array Radar Data Processing Using the Bimodal Optical Computer,” Microwave Opt. Tech. Lett. 1, 236–240 (1988).
[Crossref]

1987 (2)

M. A. G. Abushagur, H. John Caulfield, “Speed and Convergence of Bimodal Optical Computers,” Opt. Eng. 26, 022–027 (1987).
[Crossref]

M. A. G. Abushagur, H. John Caulfield, P. M. Gibson, M. A. Habli, “Superconvergence of Hybrid Optoelectronic Processors,” Appl. Opt. 26, 4906–4907 (1987).
[Crossref] [PubMed]

1986 (1)

1982 (1)

W. K. Cheng, H. J. Caulfield, “Fully Parallel Relaxation Algebraic Operations for Optical Computers,” Opt. Commun. 43, 251–254 (1982).
[Crossref]

Abushagur, M. A. G.

M. A. G. Abushagur, “Adaptive Array Radar Data Processing Using the Bimodal Optical Computer,” Microwave Opt. Tech. Lett. 1, 236–240 (1988).
[Crossref]

M. A. G. Abushagur, H. John Caulfield, “Speed and Convergence of Bimodal Optical Computers,” Opt. Eng. 26, 022–027 (1987).
[Crossref]

M. A. G. Abushagur, H. John Caulfield, P. M. Gibson, M. A. Habli, “Superconvergence of Hybrid Optoelectronic Processors,” Appl. Opt. 26, 4906–4907 (1987).
[Crossref] [PubMed]

Caulfield, H. J.

H. J. Caulfield et al., “Bimodal Optical Computers,” Appl. Opt. 25, 3128–3131 (1986).
[Crossref] [PubMed]

W. K. Cheng, H. J. Caulfield, “Fully Parallel Relaxation Algebraic Operations for Optical Computers,” Opt. Commun. 43, 251–254 (1982).
[Crossref]

Cheng, W. K.

W. K. Cheng, H. J. Caulfield, “Fully Parallel Relaxation Algebraic Operations for Optical Computers,” Opt. Commun. 43, 251–254 (1982).
[Crossref]

Gibson, P. M.

Habli, M. A.

John Caulfield, H.

M. A. G. Abushagur, H. John Caulfield, “Speed and Convergence of Bimodal Optical Computers,” Opt. Eng. 26, 022–027 (1987).
[Crossref]

M. A. G. Abushagur, H. John Caulfield, P. M. Gibson, M. A. Habli, “Superconvergence of Hybrid Optoelectronic Processors,” Appl. Opt. 26, 4906–4907 (1987).
[Crossref] [PubMed]

Scholtz, V.

V. Scholtz, E. Van Rooyen, Author: Insert Affiliation; private communication (1989).

Van Rooyen, E.

V. Scholtz, E. Van Rooyen, Author: Insert Affiliation; private communication (1989).

Appl. Opt. (2)

Microwave Opt. Tech. Lett. (1)

M. A. G. Abushagur, “Adaptive Array Radar Data Processing Using the Bimodal Optical Computer,” Microwave Opt. Tech. Lett. 1, 236–240 (1988).
[Crossref]

Opt. Commun. (1)

W. K. Cheng, H. J. Caulfield, “Fully Parallel Relaxation Algebraic Operations for Optical Computers,” Opt. Commun. 43, 251–254 (1982).
[Crossref]

Opt. Eng. (1)

M. A. G. Abushagur, H. John Caulfield, “Speed and Convergence of Bimodal Optical Computers,” Opt. Eng. 26, 022–027 (1987).
[Crossref]

Other (1)

V. Scholtz, E. Van Rooyen, Author: Insert Affiliation; private communication (1989).

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Figures (1)

Fig. 1
Fig. 1

The previous version of the bimodal optical computer utilizes a one dimensional LED array to represent the input vector and a two dimensional SLM to represent the matrix. The output vector components are detected and compared with their target values. The input vector is then adjusted to drive that difference to 0. The corresponding input vector is then evaluated digitally. This establishes a new target vector which allows the analog processor to generate a correction.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

y o = A x o
x = A - 1 b .
x t = b - A x .
x ( t ) = i { ( v i x o ) exp ( - λ i t ) + v i · b λ i [ 1 - exp ( - λ i t ) ] } v i .
x ( t ) = i ( v i · b λ i ) v i = A - 1 b .
Δ x = A H ( b - A x ) .
x t = A H b - A H A x .
v o = b - y o .
Δ x o = A T v o .
x i = x o + Δ x o

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