Zero-dimensional families of polynomial systems
If a real world problem is modelled with a system of polynomial equations, the coefficients are in general not exact. The consequence is that small perturbations of the coefficients may lead to big changes of the solutions. In this paper we address the following question: how do the zeros change whe...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Università degli Studi di Catania
2013-05-01
|
| Series: | Le Matematiche |
| Subjects: | |
| Online Access: | http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/1029 |
| id |
doaj-90418b1f2d1e4ddb827d4a5bcbf94f03 |
|---|---|
| record_format |
Article |
| spelling |
doaj-90418b1f2d1e4ddb827d4a5bcbf94f032020-11-25T02:58:35ZengUniversità degli Studi di CataniaLe Matematiche0373-35052037-52982013-05-01681137164851Zero-dimensional families of polynomial systemsLorenzo RobbianoMaria-Laura TorrenteIf a real world problem is modelled with a system of polynomial equations, the coefficients are in general not exact. The consequence is that small perturbations of the coefficients may lead to big changes of the solutions. In this paper we address the following question: how do the zeros change when the coefficients of the polynomials are perturbed? In the first part we show how to construct semi-algebraic sets in the parameter space over which the family of all ideals shares the number of isolated real zeros. In the second part we show how to modify the equations and get new ones which generate the same ideal, but whose real zeros are more stable<br />with respect to perturbations of the coefficients.<br /><br />http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/1029Algebraic familyReal zerosCondition number |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Lorenzo Robbiano Maria-Laura Torrente |
| spellingShingle |
Lorenzo Robbiano Maria-Laura Torrente Zero-dimensional families of polynomial systems Le Matematiche Algebraic family Real zeros Condition number |
| author_facet |
Lorenzo Robbiano Maria-Laura Torrente |
| author_sort |
Lorenzo Robbiano |
| title |
Zero-dimensional families of polynomial systems |
| title_short |
Zero-dimensional families of polynomial systems |
| title_full |
Zero-dimensional families of polynomial systems |
| title_fullStr |
Zero-dimensional families of polynomial systems |
| title_full_unstemmed |
Zero-dimensional families of polynomial systems |
| title_sort |
zero-dimensional families of polynomial systems |
| publisher |
Università degli Studi di Catania |
| series |
Le Matematiche |
| issn |
0373-3505 2037-5298 |
| publishDate |
2013-05-01 |
| description |
If a real world problem is modelled with a system of polynomial equations, the coefficients are in general not exact. The consequence is that small perturbations of the coefficients may lead to big changes of the solutions. In this paper we address the following question: how do the zeros change when the coefficients of the polynomials are perturbed? In the first part we show how to construct semi-algebraic sets in the parameter space over which the family of all ideals shares the number of isolated real zeros. In the second part we show how to modify the equations and get new ones which generate the same ideal, but whose real zeros are more stable<br />with respect to perturbations of the coefficients.<br /><br /> |
| topic |
Algebraic family Real zeros Condition number |
| url |
http://www.dmi.unict.it/ojs/index.php/lematematiche/article/view/1029 |
| work_keys_str_mv |
AT lorenzorobbiano zerodimensionalfamiliesofpolynomialsystems AT marialauratorrente zerodimensionalfamiliesofpolynomialsystems |
| _version_ |
1724706222209236992 |