DEQ
Fermat-Weber Problem
Computes the Fermat-Weber point UNDER CONSTRUCTION
2026.Feb.12 10:46:39
File to upload (Opt.) Optional, such as Weight.xlsx, Ones.xlsx (tables)(*).
Minimization Minimization mode.
Table Table: coordinates, weight (x, y, w).
Tol, maxiter Solution tolerance and max. iterations.
xL, xR; yM (a: auto.) Plot: left, right limits; y max. (a, autoscale)
Show values >Show graph coordinates.

Computes the "geometric median" (or Fermat-Weber point) of a set of given points in the plane. The data, for each point i = 1..n, are xi, yi, and weight wi (1 if unweighted).

The method is Weiszfeld or Python (NM) minimize.

Files involved: P.fw.php (this one), Ferweb.php, ferweb.py.

Draws the given points and their centroid and FW point.

Computation structure — A PHP file (this page: 'P.fw.php') calls (via 'action=...') an intermediate PHP file ('./Ferweb.php'), which (through $_POST) sends the problem data as command line arguments to a Python script. This last does the computing, and makes 'system' call(s) to 'gnuplot', for the final (temporary) web page.

Keywords: Geometric median; Fermat-Weber point; minimization; PHP; Python; gnuplot.
(*) If your browser does not download, try Weight.xlsx.txt, Ones.xlsx.txt and rename back.

References: Plate: FermatWeber

• (Wikipedia) PHP (from Personal Home Page); Geometric median • Symbols

• CISTI'2026, 21.ª Conferencia Ibérica de Sistemas y Tecnologías de Información (21.st Iberian Conference on Information Systems and Technologies), Santiago de Compostela (Spain), 17–20 June 2026.

• 1900-12-25: Zygmund, Antoni Szczepan (†1992-05-30, 91 yrs.).

 
 
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Created: 2025-12-25 — Last modified: 2025-12-28