Annals of Operations Research

, Volume 167, Issue 1, pp 7–41 | Cite as

On the point for which the sum of the distances to n given points is minimum

Article

Abstract

Translation with annotations of E. Weiszfeld, Sur le point pour lequel la somme des distances de n points donnés est minimum, Tôhoku Mathematical Journal (first series), 43 (1937) pp. 355–386.

A short introduction about the translation is found in Appendix A. Appendix B lists particular notations used by Weiszfeld and their now more conventional equivalents. Numbered footnotes are those of the original paper of Weiszfeld. Boxed numerals are references to observations about the translation and comments of the translator, all to be found in Appendix C.

Keywords

Location problem Weber problem Euclidean distance Weiszfeld algorithm 

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References

  1. Cánovas, L., Canavate, R., & Marín, A. (2002). On the convergence of the Weiszfeld algorithm. Mathematical Programming, 93, 327–330. CrossRefGoogle Scholar
  2. Drezner, Z., Klamroth, K., Schöbel, A., & Wesolowski, G. O. (2002). The Weber problem. In Z. Drezner & H. Hamacher (Eds.), Facility location: applications and theory (pp. 1–36). Berlin: Springer. Google Scholar
  3. Franksen, O. I., & Grattan-Guinness, I. (1989). The earliest contribution to location theory? Spatio-temporal equilibrium with Lamé and Clapeyron, 1829. Mathematics and Computers in Simulation, 31, 195–220. CrossRefGoogle Scholar
  4. Gass, S. A. (2004). In Memoriam, Andrew (Andy) Vazsonyi: 1916–2003. OR/MS Today, February 2004. http://www.lionhrtpub.com/orms/orms-2-04/frmemoriam.html, see also this volume.
  5. Hardy, G. H. (1940). A mathematician’s apology. London, now freely available at http://www.math.ualberta.ca/~mss/books/AMathematician’sApology.pdf.
  6. Kuhn, H. W., & Kuenne, R. E. (1962). An efficient algorithm for the numerical solution of the generalized Weber problem in spatial economics. Journal of Regional Science, 4, 21–33. CrossRefGoogle Scholar
  7. Kupitz, Y. S., & Martini, H. (1997). Geometric aspects of the generalized Fermat-Torricelli problem. In Mathematical studies: Vol. 6. Intuitive geometry (pp. 55–127). Bolyai Society. Google Scholar
  8. Lamé, G., & Clapeyron, B. P. E. (1829). Mémoire sur l’application de la statique à la solution des problèmes relatifs à la théorie des moindres distances. Journal des Voies de Communications, 10, 26–49. (In french—Memoir on the application of statics to the solution of problems concerning the theory of least distances.) For a translation into English see Franksen, O.I., Grattan-Guinness, I. (1989). Mathematics and Computers in Simulation, 31, 195–220. Google Scholar
  9. Sturm, R. (1884). Ueber den Punkt kleinster Entfernungssumme von gegebenen Punkten. Journal für die reine und angewandte Mathematik, 97, 49–61. (In german—On the point of smallest distance sum from given points). CrossRefGoogle Scholar
  10. Vazsonyi, A. (2002a). Which door has the Cadillac. New York: Writers Club Press. Google Scholar
  11. Vazsonyi, A. (2002b). Pure mathematics and the Weiszfeld algorithm. Decision Line, 33(3), 12–13. http://www.decisionsciences.org/DecisionLine/Vol33/33_3/index.htm. Google Scholar
  12. Weiszfeld, E. (1936). Sur un problème de minimum dans l’espace. Tôhoku Mathematical Journal, 42, 274–280. (First series). Google Scholar
  13. Weiszfeld, E. (1937). Sur le point pour lequel la somme des distances de n points donnés est minimum. Tôhoku Mathematical Journal, 43, 355–386. (First series). Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of Mathematics, Operational Research, Statistics and Information Systems for Management MOSIVrije Universiteit BrusselBrusselsBelgium

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