Verified Error Bounds for Isolated Singular Solutions of Polynomial Systems
Nan Li, Lihong Zhi · SIAM Journal on Numerical Analysis · 2014
In this paper, we generalize the algorithm described by Rump and Graillat, as well as our previous work on verifying breadth-one singular solutions of polynomial systems, to compute verified and narrow error bounds such that a slightly perturbed system is guaranteed to possess an isolated singular solution within computed error bounds. Our verification method is based on deflation techniques using smoothing parameters. We demonstrate the performance of the algorithm for polynomial systems with singular solutions of multiplicity up to hundreds.