Verified error bounds for isolated singular solutions of polynomial systems: Case of breadth one

In this paper we describe how to improve the performance of the symbolic–numeric method in [19,20] for computing the multiplicity structure and refining approximate isolated singular solutions in the breadth-one case. By introducing a parameterized deflated system with smoothing parameters, we generalize the algorithm in [33] 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.