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.
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Cánovas, L., Canavate, R., & Marín, A. (2002). On the convergence of the Weiszfeld algorithm. Mathematical Programming, 93, 327–330.
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.
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.
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.
Hardy, G. H. (1940). A mathematician’s apology. London, now freely available at http://www.math.ualberta.ca/~mss/books/AMathematician’sApology.pdf.
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.
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.
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.
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).
Vazsonyi, A. (2002a). Which door has the Cadillac. New York: Writers Club Press.
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.
Weiszfeld, E. (1936). Sur un problème de minimum dans l’espace. Tôhoku Mathematical Journal, 42, 274–280. (First series).
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).
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Translated and annotated by Frank Plastria.
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Weiszfeld, E., Plastria, F. On the point for which the sum of the distances to n given points is minimum. Ann Oper Res 167, 7–41 (2009). https://doi.org/10.1007/s10479-008-0352-z
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DOI: https://doi.org/10.1007/s10479-008-0352-z