Abstract
We consider polynomial systems of Prony type, appearing in many areas of mathematics. Their robust numerical solution is considered to be difficult, especially in “near-colliding” situations. We consider a case when the structure of the system is a-priori fixed. We transform the nonlinear part of the Prony system into a Hankel-type polynomial system. Combining this representation with a recently discovered “decimation” technique, we present an algorithm which applies homotopy continuation to an appropriately chosen Hankel-type system as above. In this way, we are able to solve for the nonlinear variables of the original system with high accuracy when the data is perturbed.
Original language | English |
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Pages (from-to) | 27-40 |
Number of pages | 14 |
Journal | Theoretical Computer Science |
Volume | 681 |
DOIs | |
State | Published - 12 Jun 2017 |
Externally published | Yes |
Keywords
- Decimation
- ESPRIT
- Homotopy continuation
- Polynomial systems
- Prony system