A Stochastic Newton-Raphson Method with Noisy Function Measurements
This letter shows that traditional Newton-Raphson (NR) method cannot achieve zero-convergence in presence of additive noise without adding a multiplicative gain. Furthermore, this gain needs to converge to zero. This article proposes a novel recursive algorithm providing optimal iterative-varying ga...
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2016
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| Online Access: | http://hdl.handle.net/10725/11180 http://dx.doi.org/10.1109/LSP.2015.2511456 http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php https://ieeexplore.ieee.org/abstract/document/7364187 |
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| _version_ | 1864513488341172224 |
|---|---|
| author | Saab, Khaled Kamal |
| author2 | Saab, Samer Said |
| author2_role | author |
| author_facet | Saab, Khaled Kamal Saab, Samer Said |
| author_role | author |
| dc.creator.none.fl_str_mv | Saab, Khaled Kamal Saab, Samer Said |
| dc.date.none.fl_str_mv | 2016 2019-07-31T10:51:43Z 2019-07-31T10:51:43Z 2019-07-31 |
| dc.identifier.none.fl_str_mv | 1070-9908 http://hdl.handle.net/10725/11180 http://dx.doi.org/10.1109/LSP.2015.2511456 Saab, K. K., & Saab, S. S. (2015). A stochastic Newton-Raphson method with noisy function measurements. IEEE signal processing letters, 23(3), 361-365. http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php https://ieeexplore.ieee.org/abstract/document/7364187 |
| dc.language.none.fl_str_mv | en |
| dc.relation.none.fl_str_mv | IEEE Signal Processing Letters |
| dc.rights.*.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.title.none.fl_str_mv | A Stochastic Newton-Raphson Method with Noisy Function Measurements |
| dc.type.none.fl_str_mv | Article info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | This letter shows that traditional Newton-Raphson (NR) method cannot achieve zero-convergence in presence of additive noise without adding a multiplicative gain. Furthermore, this gain needs to converge to zero. This article proposes a novel recursive algorithm providing optimal iterative-varying gains associated with the NR method. The development of the proposed optimal algorithm is based on minimizing a stochastic performance index. The estimation error covariance matrix is shown to converge to zero for linearized functions while considering additive zero-mean white noise. In addition, the proposed approach is capable of overcoming common drawbacks associated with the traditional NR method. Simulation results are included to illustrate the performance capabilities of the proposed algorithm. We show that the proposed recursive algorithm provides significant improvement over the traditional NR method. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | LAURepo_0bbc3158e87fb2273d1a8a52dfa13d91 |
| identifier_str_mv | 1070-9908 Saab, K. K., & Saab, S. S. (2015). A stochastic Newton-Raphson method with noisy function measurements. IEEE signal processing letters, 23(3), 361-365. |
| language_invalid_str_mv | en |
| network_acronym_str | LAURepo |
| network_name_str | Lebanese American University repository |
| oai_identifier_str | oai:laur.lau.edu.lb:10725/11180 |
| publishDate | 2016 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
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| spelling | A Stochastic Newton-Raphson Method with Noisy Function MeasurementsSaab, Khaled KamalSaab, Samer SaidThis letter shows that traditional Newton-Raphson (NR) method cannot achieve zero-convergence in presence of additive noise without adding a multiplicative gain. Furthermore, this gain needs to converge to zero. This article proposes a novel recursive algorithm providing optimal iterative-varying gains associated with the NR method. The development of the proposed optimal algorithm is based on minimizing a stochastic performance index. The estimation error covariance matrix is shown to converge to zero for linearized functions while considering additive zero-mean white noise. In addition, the proposed approach is capable of overcoming common drawbacks associated with the traditional NR method. Simulation results are included to illustrate the performance capabilities of the proposed algorithm. We show that the proposed recursive algorithm provides significant improvement over the traditional NR method.PublishedN/A2019-07-31T10:51:43Z2019-07-31T10:51:43Z20162019-07-31Articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article1070-9908http://hdl.handle.net/10725/11180http://dx.doi.org/10.1109/LSP.2015.2511456Saab, K. K., & Saab, S. S. (2015). A stochastic Newton-Raphson method with noisy function measurements. IEEE signal processing letters, 23(3), 361-365.http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.phphttps://ieeexplore.ieee.org/abstract/document/7364187enIEEE Signal Processing Lettersinfo:eu-repo/semantics/openAccessoai:laur.lau.edu.lb:10725/111802021-03-19T10:47:36Z |
| spellingShingle | A Stochastic Newton-Raphson Method with Noisy Function Measurements Saab, Khaled Kamal |
| status_str | publishedVersion |
| title | A Stochastic Newton-Raphson Method with Noisy Function Measurements |
| title_full | A Stochastic Newton-Raphson Method with Noisy Function Measurements |
| title_fullStr | A Stochastic Newton-Raphson Method with Noisy Function Measurements |
| title_full_unstemmed | A Stochastic Newton-Raphson Method with Noisy Function Measurements |
| title_short | A Stochastic Newton-Raphson Method with Noisy Function Measurements |
| title_sort | A Stochastic Newton-Raphson Method with Noisy Function Measurements |
| url | http://hdl.handle.net/10725/11180 http://dx.doi.org/10.1109/LSP.2015.2511456 http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php https://ieeexplore.ieee.org/abstract/document/7364187 |