Name
Abstract | ||
|---|---|---|
We present a modification of Newton's method to restore quadratic convergence for isolated singular solutions of polynomial systems. Our method is symbolic-numeric: we produce a new polynomial system which has the original multiple solution as a regular root. Using standard bases, a tool for the symbolic computation of multiplicities, we show that the number of deflation stages is bounded by the multiplicity of the isolated root. Our implementation performs well on a large class of applications. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1016/j.tcs.2006.02.018 | Theor. Comput. Sci. |
Keywords | DocType | Volume |
regular root,new polynomial system,deflation stage,large class,isolated singular solution,Newton's method,Deflation,secondary,68W30,original multiple solution,quadratic convergence,polynomial system,symbolic-numeric computations,14Q99,Symbolic–numeric computations,reconditioning,numerical homotopy algorithms,deflation,standard base,primary,Numerical homotopy algorithms,isolated root,Reconditioning,isolated singularity,newton's method,65H10 | Journal | 359 |
Issue | ISSN | Citations |
1 | Theoretical Computer Science | 61 |
PageRank | References | Authors |
3.07 | 20 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Anton Leykin | 1 | 173 | 18.99 |
| Jan Verschelde | 2 | 676 | 64.84 |
| Ailing Zhao | 3 | 61 | 3.07 |