A Note on Algorithms for Determining the Copositivity of a Given Symmetric Matrix
<p/> <p>In the previous paper by the first and the third authors, we present six algorithms for determining whether a given symmetric matrix is strictly copositive, copositive (but not strictly), or not copositive. The algorithms for matrices of order <inline-formula> <graphic f...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2010/498631 |
| _version_ | 1811299804388524032 |
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| author | Chang-qing Xu Xiao-xin Li Shang-jun Yang |
| author_facet | Chang-qing Xu Xiao-xin Li Shang-jun Yang |
| author_sort | Chang-qing Xu |
| collection | DOAJ |
| description | <p/> <p>In the previous paper by the first and the third authors, we present six algorithms for determining whether a given symmetric matrix is strictly copositive, copositive (but not strictly), or not copositive. The algorithms for matrices of order <inline-formula> <graphic file="1029-242X-2010-498631-i1.gif"/></inline-formula> are not guaranteed to produce an answer. It also shows that for 1000 symmetric random matrices of order 8, 9, and 10 with unit diagonal and with positive entries all being less than or equal to 1 and negative entries all being greater than or equal to <inline-formula> <graphic file="1029-242X-2010-498631-i2.gif"/></inline-formula>, there are 8, 6, and 2 matrices remaing undetermined, respectively. In this paper we give two more algorithms for <inline-formula> <graphic file="1029-242X-2010-498631-i3.gif"/></inline-formula> and our experiment shows that no such matrix of order 8 or 9 remains undetermined; and almost always no such matrix of order 10 remains undetermined. We also do some discussion based on our experimental results.</p> |
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| format | Article |
| id | doaj.art-8cdc3794306441669b5e7f5518db03c6 |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-04-13T06:41:15Z |
| publishDate | 2010-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-8cdc3794306441669b5e7f5518db03c62022-12-22T02:57:43ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2010-01-0120101498631A Note on Algorithms for Determining the Copositivity of a Given Symmetric MatrixChang-qing XuXiao-xin LiShang-jun Yang<p/> <p>In the previous paper by the first and the third authors, we present six algorithms for determining whether a given symmetric matrix is strictly copositive, copositive (but not strictly), or not copositive. The algorithms for matrices of order <inline-formula> <graphic file="1029-242X-2010-498631-i1.gif"/></inline-formula> are not guaranteed to produce an answer. It also shows that for 1000 symmetric random matrices of order 8, 9, and 10 with unit diagonal and with positive entries all being less than or equal to 1 and negative entries all being greater than or equal to <inline-formula> <graphic file="1029-242X-2010-498631-i2.gif"/></inline-formula>, there are 8, 6, and 2 matrices remaing undetermined, respectively. In this paper we give two more algorithms for <inline-formula> <graphic file="1029-242X-2010-498631-i3.gif"/></inline-formula> and our experiment shows that no such matrix of order 8 or 9 remains undetermined; and almost always no such matrix of order 10 remains undetermined. We also do some discussion based on our experimental results.</p>http://www.journalofinequalitiesandapplications.com/content/2010/498631 |
| spellingShingle | Chang-qing Xu Xiao-xin Li Shang-jun Yang A Note on Algorithms for Determining the Copositivity of a Given Symmetric Matrix Journal of Inequalities and Applications |
| title | A Note on Algorithms for Determining the Copositivity of a Given Symmetric Matrix |
| title_full | A Note on Algorithms for Determining the Copositivity of a Given Symmetric Matrix |
| title_fullStr | A Note on Algorithms for Determining the Copositivity of a Given Symmetric Matrix |
| title_full_unstemmed | A Note on Algorithms for Determining the Copositivity of a Given Symmetric Matrix |
| title_short | A Note on Algorithms for Determining the Copositivity of a Given Symmetric Matrix |
| title_sort | note on algorithms for determining the copositivity of a given symmetric matrix |
| url | http://www.journalofinequalitiesandapplications.com/content/2010/498631 |
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