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H. Fritz, P. Filzmoser, C. Croux:
"A comparison of algorithms for the multivariate L1-median";
Computational Statistics, 27 (2012), 393 - 410.

The L1-median is a robust estimator of multivariate location with good statistical properties. Several algorithms for computing the L1-median are available. Problem specific algorithms can be used, but also general optimization routines. The aim is to compare different algorithms with respect to their precision and runtime. This is possible because all considered algorithms have been implemented in a standardized manner in the open source environment R. In most situations, the algorithm based on the optimization routine NLM (non-linear minimization) clearly outperforms other approaches. Its low computation time makes applications for large and high-dimensional data feasible.

http://dx.doi.org/10.1007/s00180-011-0262-4

http://link.springer.com/article/10.1007%2Fs00180-011-0262-4?LI=true