# Computing Isolated Singular Solutions of Polynomial Systems: Case of Breadth One - Mathematics > Numerical Analysis

Abstract: We present a symbolic-numeric method to refine an approximate isolatedsingular solution $\hat{\mathbf{x}}=\hat{x} {1}, ., \hat{x} {n}$ of apolynomial system $F=\{f 1, ., f n\}$ when the Jacobian matrix of $F$evaluated at $\hat{\mathbf{x}}$ has corank one approximately. Our new approachis based on the regularized Newton iteration and the computation of approximateMax Noether conditions satisfied at the approximate singular solution. The sizeof matrices involved in our algorithm is bounded by $n \times n$. The algorithmconverges quadratically if $\hat{\xx}$ is close to the isolated exact singularsolution.

Author: Nan Li, Lihong Zhi

Source: https://arxiv.org/