Embedding Method by Real Numerical Algebraic Geometry for Structurally Unamenable Differential-Algebraic Equations
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2021
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909067224547328 |
|---|---|
| author | Yang, Wenqiang Wu, Wenyuan Reid, Greg |
| author_facet | Yang, Wenqiang Wu, Wenyuan Reid, Greg |
| contents | Existing structural analysis methods may fail to find all hidden constraints for a system of differential-algebraic equations with parameters if the system is structurally unamenable for certain values of the parameters.
In this paper, for polynomial systems of differential-algebraic equations, numerical methods are given to solve such cases using numerical real algebraic geometry. First, we propose an embedding method that for a given real analytic system constructs an equivalent system with a full-rank Jacobian matrix. Secondly, we introduce a witness point method, which can help to detect degeneration on all components of constraints of such systems. Thirdly, the two methods above lead to a numerical global structural analysis method for structurally unamenable differential-algebraic equations on all components of constraints. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_08160 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Embedding Method by Real Numerical Algebraic Geometry for Structurally Unamenable Differential-Algebraic Equations Yang, Wenqiang Wu, Wenyuan Reid, Greg Numerical Analysis Dynamical Systems Existing structural analysis methods may fail to find all hidden constraints for a system of differential-algebraic equations with parameters if the system is structurally unamenable for certain values of the parameters. In this paper, for polynomial systems of differential-algebraic equations, numerical methods are given to solve such cases using numerical real algebraic geometry. First, we propose an embedding method that for a given real analytic system constructs an equivalent system with a full-rank Jacobian matrix. Secondly, we introduce a witness point method, which can help to detect degeneration on all components of constraints of such systems. Thirdly, the two methods above lead to a numerical global structural analysis method for structurally unamenable differential-algebraic equations on all components of constraints. |
| title | Embedding Method by Real Numerical Algebraic Geometry for Structurally Unamenable Differential-Algebraic Equations |
| topic | Numerical Analysis Dynamical Systems |
| url | https://arxiv.org/abs/2111.08160 |