id: 06430506
dt: j
an:
au: Jankov Maširević, Dragana; Miodragović, Suzana
ti: Geometric median in the plane.
so: Elem. Math. 70, No. 1, 21-32 (2015).
py: 2015
pu: European Mathematical Society (EMS) Publishing House, Zurich
la: EN
cc: G45
ut:
ci:
li: http://www.ems-ph.org/journals/show_pdf.php?vol=70&iss=1&issn=0013-6018&rank=4
ab: Given $\{T_i,1\leq i\leq m\}$ a set of points in the plane with
corresponding weights $w_i>0$, the weighted geometric median of these
points is the point $T$ minimizing the sum of the weighted Euclidean
distances from $T$ to the previous points. In this paper, the authors
study the problem of determining the geometric median of three points;
i.e., the weighted geometric median with all weights equal to 1. In
particular they relate this point to the Torricelli point of the
triangle formed by the three points (provided they are not collinear).
This is done by purely geometric techniques. For higher dimensional
settings, the authors translate the geometric problem to that of
minimizing a functional $F:\mathbb{R}^2\rightarrow\mathbb{R}$. To do so
they apply Weiszfeld’s algorithm. Finally, some examples are given.
rv: Antonio M. Oller (Zaragoza)