OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 33, Iss. 13 — May. 1, 1994
  • pp: 2411–2418

Determination method of an initial damping factor in the damped-least-squares problem

Hiroshi Matsui and Kazuo Tanaka  »View Author Affiliations


Applied Optics, Vol. 33, Issue 13, pp. 2411-2418 (1994)
http://dx.doi.org/10.1364/AO.33.002411


View Full Text Article

Enhanced HTML    Acrobat PDF (728 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

By analyzing the relationship between eigenvalues of the product of the Jacobian matrix of performance functions and a damping factor, we believe that we have developed a new analytical method for setting an adequate initial value for the damping factor in the damped least-squares problem. The value of a damping factor should be almost that of a median of the eigenvalues. The effectiveness of the method is shown by some numerical experiments.

© 1994 Optical Society of America

History
Original Manuscript: April 6, 1993
Published: May 1, 1994

Citation
Hiroshi Matsui and Kazuo Tanaka, "Determination method of an initial damping factor in the damped-least-squares problem," Appl. Opt. 33, 2411-2418 (1994)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-33-13-2411


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. T. H. Jamieson, Optimization Techniques in Lens Design (Hilger, London, 1971).
  2. A. K. Rigler, R. J. Pegis, “Optimization methods in optics,” in The Computer in Optical Research—Methods and Applications (Springer-Verlag, Berlin, 1980), pp. 211–268.
  3. K. A. Levenberg, “A method for the solution of certain nonlinear problems in least squares,” Q. J. Appl. Math. 2, 164–168 (1944).
  4. D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” J. Soc. Ind. Appl. Math. 11, 431–441 (1963). [CrossRef]
  5. A. Girard, “Calcul automatique en optique geometrique,” Rev. Opt. 37, 225–241 (1958).
  6. C. G. Wynne, “Lens designing by electronic digital computer I,” Proc. Phys. Soc. London 73, 777–787 (1959). [CrossRef]
  7. C. G. Wynne, P. M. J. H. Wormell, “Lens design by computer,” Appl. Opt. 2, 1233–1238 (1963). [CrossRef]
  8. Ref. 1, pp. 61–62.
  9. M. J. Kidger, C. G. Wynne, “Experiments with lens optimization procedures,” Opt. Acta 14, 279–288 (1967). [CrossRef]
  10. D. F. Shanno, “Parameter solution for modified Newton methods for function minimization,” SLAM J. Numer. Anal. 7, 366–372 (1970). [CrossRef]
  11. A. Jones, “Spiral—a new algorithm for nonlinear parameter estimation using least squares,” Comput. J. 13, 301–308 (1970). [CrossRef]
  12. J. Meiron, “Damped least-squares method for automatic lens design,” J. Opt. Soc. Am. 55, 1105–1109 (1965). [CrossRef]
  13. D. R. Buchele, “Damping factor for the least-squares method of optical design,” Appl. Opt. 7, 2433–2435 (1968). [CrossRef] [PubMed]
  14. H. Matsui, K. Tanaka, “Solution of the damped least-squares problem by using a combination of eigenvalue and singular value decompositions,” Appl. Opt. 31, 2241–2243 (1992). [CrossRef] [PubMed]
  15. G. H. Golub, C. Reinsch, “Singular value decomposition and least-squares solutions,” Numer. Math. 14, 403–420 (1970). [CrossRef]
  16. For example, see C. L. Lawson, R. J. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, N. J., 1974), p. 237.
  17. For example, see W. T. Welford, Aberrations of the Symmetrical Optical System (Academic, London, 1974), p. 192.
  18. Y. Matsui, Theory of Lens Design (Kyoritsu, Tokyo, 1972), pp. 114–119 (in Japanese).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited