The largest eigenvalue of nonnegative tensors
In this thesis we study the methods for finding the largest eigenvalue of tensors. In particular, we study the convergence of the methods and show that the method for rectangular tensors is Q-linear convergence under weak irreducibility condition. We further generalise the method to nonnegative poly...
| Main Author: | |
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| Format: | Thesis |
| Language: | English |
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Curtin University
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/2007 |
| _version_ | 1848743832371331072 |
|---|---|
| author | Ibrahim, Nur Fadhilah |
| author_facet | Ibrahim, Nur Fadhilah |
| author_sort | Ibrahim, Nur Fadhilah |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this thesis we study the methods for finding the largest eigenvalue of tensors. In particular, we study the convergence of the methods and show that the method for rectangular tensors is Q-linear convergence under weak irreducibility condition. We further generalise the method to nonnegative polynomial eigenvalue problems. We prove that this method is convergent for nonhomogeneous irreducible nonnegative polynomials. Then, we apply this method to solve nonnegative polynomial optimization problems with spherical constraints. |
| first_indexed | 2025-11-14T05:51:50Z |
| format | Thesis |
| id | curtin-20.500.11937-2007 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T05:51:50Z |
| publishDate | 2013 |
| publisher | Curtin University |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-20072017-02-20T06:39:12Z The largest eigenvalue of nonnegative tensors Ibrahim, Nur Fadhilah In this thesis we study the methods for finding the largest eigenvalue of tensors. In particular, we study the convergence of the methods and show that the method for rectangular tensors is Q-linear convergence under weak irreducibility condition. We further generalise the method to nonnegative polynomial eigenvalue problems. We prove that this method is convergent for nonhomogeneous irreducible nonnegative polynomials. Then, we apply this method to solve nonnegative polynomial optimization problems with spherical constraints. 2013 Thesis http://hdl.handle.net/20.500.11937/2007 en Curtin University fulltext |
| spellingShingle | Ibrahim, Nur Fadhilah The largest eigenvalue of nonnegative tensors |
| title | The largest eigenvalue of nonnegative tensors |
| title_full | The largest eigenvalue of nonnegative tensors |
| title_fullStr | The largest eigenvalue of nonnegative tensors |
| title_full_unstemmed | The largest eigenvalue of nonnegative tensors |
| title_short | The largest eigenvalue of nonnegative tensors |
| title_sort | largest eigenvalue of nonnegative tensors |
| url | http://hdl.handle.net/20.500.11937/2007 |