## A Newton acceleration of the Weiszfeld algorithm for minimizing the sum of Euclidean distances |

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Advanced Computing Research akdk algorithm in FIG Assume bandwidth Cholesky factorization coinciding locations convergence analysis convex function definite band matrix denote descent direction diag diag(r diagonal matrix dimension Euclidean location problem Euclidean norms Example existing locations Fadil Santosa fast local convergence fix the number full row rank gkTdk Hessian Hk Hessian matrix interior point method large-scale problems least squares problem least squares solve LEMMA limit point line search linear programming problems main computation Matlab MINIMIZING THE SUM multifacility location problem Newton acceleration Newton process Newton step 11 nloc nondifferentiability nonlinear system number of existing number of iterations objective function parallel computer performance of N-Weiszfeld positive definite band proposed N-Weiszfeld algorithm Random Multifacility Location RMFL solution solving a weighted sum of Euclidean symmetric positive definite tloc Trust Region vary the number Wei Yuan weighted least squares weights are set Weiszfeld algorithm Weiszfeld step Xk+l Yuying zero