Name
Abstract | ||
|---|---|---|
We develop a new symbolic-numeric algorithm for the certification of singular isolated points, using their associated local ring structure and certified numerical computations. An improvement of an existing method to compute inverse systems is presented, which avoids redundant computation and reduces the size of the intermediate linear systems to solve. We derive a one-step deflation technique, from the description of the multiplicity structure in terms of differentials. The deflated system can be used in Newton-based iterative schemes with quadratic convergence. Starting from a polynomial system and a sufficiently small neighborhood, we obtain a criterion for the existence and uniqueness of a singular root of a given multiplicity structure, applying a well-chosen symbolic perturbation. Standard verification methods, based e.g. on interval arithmetic and a fixed point theorem, are employed to certify that there exists a unique perturbed system with a singular root in the domain. Applications to topological degree computation and to the analysis of real branches of an implicit curve illustrate the method. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1145/1993886.1993925 | international symposium on symbolic and algebraic computation |
Keywords | DocType | Volume |
singular zero,root deflation,certified isolation,deflated system,certified numerical computation,inverse system,polynomial system,intermediate linear system,isolated point,inverse sys- tem,dual space,multiplicity structure,singular isolated point,degree computation,singular root,associated local ring structure,fixed point theorem,interval arithmetic,quadratic convergence,linear system | Conference | abs/1101.3140 |
Citations | PageRank | References |
18 | 0.74 | 12 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Angelos Mantzaflaris | 1 | 82 | 11.47 |
| Bernard Mourrain | 2 | 1074 | 113.70 |