A globally and quadratically convergent method for absolute value equations
We investigate the NP-hard absolute value equation (AVE) Ax−|x|=b, where A is an arbitrary n×n real matrix. In this paper, we propose a smoothing Newton method for the AVE. When the singular values of A exceed 1, we show that this proposed method is globally convergent and the convergence rate is qu...
| Main Authors: | , , |
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| Format: | Journal Article |
| Published: |
Springer, Van Godewijckstraat
2011
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| Online Access: | http://hdl.handle.net/20.500.11937/30213 |
| _version_ | 1848753024061669376 |
|---|---|
| author | Caccetta, Louis Qu, B. Zhou, Guanglu |
| author_facet | Caccetta, Louis Qu, B. Zhou, Guanglu |
| author_sort | Caccetta, Louis |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | We investigate the NP-hard absolute value equation (AVE) Ax−|x|=b, where A is an arbitrary n×n real matrix. In this paper, we propose a smoothing Newton method for the AVE. When the singular values of A exceed 1, we show that this proposed method is globally convergent and the convergence rate is quadratic. Preliminary numerical results show that this method is promising. |
| first_indexed | 2025-11-14T08:17:56Z |
| format | Journal Article |
| id | curtin-20.500.11937-30213 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:17:56Z |
| publishDate | 2011 |
| publisher | Springer, Van Godewijckstraat |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-302132017-09-13T16:08:46Z A globally and quadratically convergent method for absolute value equations Caccetta, Louis Qu, B. Zhou, Guanglu We investigate the NP-hard absolute value equation (AVE) Ax−|x|=b, where A is an arbitrary n×n real matrix. In this paper, we propose a smoothing Newton method for the AVE. When the singular values of A exceed 1, we show that this proposed method is globally convergent and the convergence rate is quadratic. Preliminary numerical results show that this method is promising. 2011 Journal Article http://hdl.handle.net/20.500.11937/30213 10.1007/s10589-009-9242-9 Springer, Van Godewijckstraat restricted |
| spellingShingle | Caccetta, Louis Qu, B. Zhou, Guanglu A globally and quadratically convergent method for absolute value equations |
| title | A globally and quadratically convergent method for absolute value equations |
| title_full | A globally and quadratically convergent method for absolute value equations |
| title_fullStr | A globally and quadratically convergent method for absolute value equations |
| title_full_unstemmed | A globally and quadratically convergent method for absolute value equations |
| title_short | A globally and quadratically convergent method for absolute value equations |
| title_sort | globally and quadratically convergent method for absolute value equations |
| url | http://hdl.handle.net/20.500.11937/30213 |