  We present new algorithms for $M$-estimators of multivariate scatter and
location and for symmetrized $M$-estimators of multivariate scatter. The new
algorithms are considerably faster than currently used fixed-point and related
algorithms. The main idea is to utilize a second order Taylor expansion of the
target functional and to devise a partial Newton-Raphson procedure. In
connection with symmetrized $M$-estimators we work with incomplete
$U$-statistics to accelerate our procedures initially.
