THE MODIFIED FORM OF WEISZFELD’S ALGORITHM Author information + 文章历史 + 摘要 设R~n是n维欧氏空间,w_i(i=1,…,m)是m个正数,||·||表示欧氏范数.著名的Fermat-Weber场址问题是 Abstract For the Fermat-Weber location problem, Kuhn (1973) claimed that if the mgiven points are not col...
Using ideas for stabilizing the classical Weiszfeld algorithm at anchor points and the Kurdyka鈥搊jasiewicz property of the energy functional, we prove global convergence of the whole sequence of iterates generated by the algorithm to a critical point of the energy functional. Numerical examples ...
The function doesn't work anyway, even for straight up geometric medians of non-geographic multi-points. I calculated the geometric median for a few thousand sample test multi-points from my database, and summed the distance versus a random point to make sure the random point was never a b...
For solving the Euclidean distance Weber problem Weiszfeld proposed an iterative method. This method can also be applied to generalized Weber problems in Banach spaces. Examples for generalized Weber problems are: minimal surfaces with obstacles, Fermat's principle in geometrical optics and brachistochrone...
// implements the solving algorithm void go() { // start by finding the sum of distances to the center of gravity double d = dist(x, y); // our step value, chosen by experimentation double step = 100.0; // done is used to keep track of updates: if none of the neighbors of the...
algorithmThe Weber problem consists of finding a point in R n that minimizes the weighted sum of distances from m points in R n that are not collinear. An application that motivated this problem is the optimal location of facilities in the 2-dimensional case. A classical method to solve the...
A. I. MatasovSP MAIK Nauka/InterperiodicaP. A. Akimov , A. I. Matasov, Levels of nonoptimality of the Weiszfeld Algorithm in the least-modules method, Automation and Remote Control, v.71 n.2, p.172-184, February 2010 [doi>10.1134/S0005117910020025]...
Projected Weiszfeld algorithmSpectral demixingWeiszfeld's method provides an efficient way for computing the weighted median of anchor points $$p_j \\\in {\\\mathbb {R}}^n$$, $$j=1,\\\ldots ,M$$, i.e., the minimizer of $$\\\sum _{j=1}^M w_j \\\Vert x-p_j\\\Vdoi:...
In this chapter we analyze the behavior of Weiszfeld's method for solving the Fermat–Weber location problem. We show that the algorithm generates a good approximate solution, if computational errors...doi:10.1007/978-3-319-30921-7_6Alexander J. Zaslavski...
doi:10.1134/S0005117910020025P. A. AkimovA. I. MatasovSP MAIK Nauka/InterperiodicaAutomation & Remote ControlP. A. Akimov , A. I. Matasov, Levels of nonoptimality of the Weiszfeld Algorithm in the least-modules method, Automation and Remote Control, v.71 n.2, p.172-184, February ...