  In this paper we describe how to improve the performance of the
symbolic-numeric method in (Li and Zhi,2009, 2011) for computing the
multiplicity structure and refining approximate isolated singular solutions in
the breadth one case. By introducing a parameterized and deflated system with
smoothing parameters, we generalize the algorithm in (Rump and Graillat, 2009)
to compute verified error bounds such that a slightly perturbed polynomial
system is guaranteed to have a breadth-one multiple root within the computed
bounds.
