Abstract
We present a symbolic-numeric method to refine an approximate isolated singular solution $\hat{\mathbf{x}}=(\hat{x}_{1}, \ldots, \hat{x}_{n})$ of a polynomial system $F=\{f_1, \ldots, f_n\}$, when the Jacobian matrix of $F$ evaluated at $\hat{\mathbf{x}}$ has corank one approximately. Our new approach is based on the regularized Newton iteration and the computation of differential conditions satisfied at the approximate singular solution. The size of matrices involved in our algorithm is bounded by $n \times n$. The algorithm converges quadratically if $\hat{\mathbf{x}}$ is close to the isolated exact singular solution.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
