The purpose of this note is to extend the results on uniform smoothed analysis of condition numbers from \cite{ BuCuLo:07} to the case where the perturbation follows a radially symmetric probability distribution. In particular, we will show that the bounds derived in \cite{ BuCuLo:07} still hold in the case of distributions whose density has a singularity at the center of the perturbation, which we call { \em adversarial}.
Categories: math.NA math.PR