Nonrecursive Equivalent of the Conjugate Gradient Method without the Need to Restart
A simple alternative to the conjugate gradient (CG) method is presented; this method is developed as a special case of the more general iterated Ritz method (IRM) for solving a system of linear equations. This novel algorithm is not based on conjugacy; i.e., it is not necessary to maintain overall o...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Advances in Civil Engineering |
| Online Access: | http://dx.doi.org/10.1155/2019/7527590 |
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| _version_ | 1832562460886827008 |
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| author | Josip Dvornik Damir Lazarevic Antonia Jaguljnjak Lazarevic Marija Demsic |
| author_facet | Josip Dvornik Damir Lazarevic Antonia Jaguljnjak Lazarevic Marija Demsic |
| author_sort | Josip Dvornik |
| collection | DOAJ |
| description | A simple alternative to the conjugate gradient (CG) method is presented; this method is developed as a special case of the more general iterated Ritz method (IRM) for solving a system of linear equations. This novel algorithm is not based on conjugacy; i.e., it is not necessary to maintain overall orthogonalities between various vectors from distant steps. This method is more stable than CG, and restarting techniques are not required. As in CG, only one matrix-vector multiplication is required per step with appropriate transformations. The algorithm is easily explained by energy considerations without appealing to the A-orthogonality in n-dimensional space. Finally, relaxation factor and preconditioning-like techniques can be adopted easily. |
| format | Article |
| id | doaj-art-388f2be965094870b50c98ed96355d49 |
| institution | Kabale University |
| issn | 1687-8086 1687-8094 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Civil Engineering |
| spelling | doaj-art-388f2be965094870b50c98ed96355d492025-02-03T01:22:30ZengWileyAdvances in Civil Engineering1687-80861687-80942019-01-01201910.1155/2019/75275907527590Nonrecursive Equivalent of the Conjugate Gradient Method without the Need to RestartJosip Dvornik0Damir Lazarevic1Antonia Jaguljnjak Lazarevic2Marija Demsic3University of Zagreb, Faculty of Civil Engineering, Kaciceva 26, Zagreb 10 000, CroatiaUniversity of Zagreb, Faculty of Civil Engineering, Kaciceva 26, Zagreb 10 000, CroatiaUniversity of Zagreb, Faculty of Mining, Geology and Petroleum Engineering, Pierottijeva 6, Zagreb 10 000, CroatiaUniversity of Zagreb, Faculty of Civil Engineering, Kaciceva 26, Zagreb 10 000, CroatiaA simple alternative to the conjugate gradient (CG) method is presented; this method is developed as a special case of the more general iterated Ritz method (IRM) for solving a system of linear equations. This novel algorithm is not based on conjugacy; i.e., it is not necessary to maintain overall orthogonalities between various vectors from distant steps. This method is more stable than CG, and restarting techniques are not required. As in CG, only one matrix-vector multiplication is required per step with appropriate transformations. The algorithm is easily explained by energy considerations without appealing to the A-orthogonality in n-dimensional space. Finally, relaxation factor and preconditioning-like techniques can be adopted easily.http://dx.doi.org/10.1155/2019/7527590 |
| spellingShingle | Josip Dvornik Damir Lazarevic Antonia Jaguljnjak Lazarevic Marija Demsic Nonrecursive Equivalent of the Conjugate Gradient Method without the Need to Restart Advances in Civil Engineering |
| title | Nonrecursive Equivalent of the Conjugate Gradient Method without the Need to Restart |
| title_full | Nonrecursive Equivalent of the Conjugate Gradient Method without the Need to Restart |
| title_fullStr | Nonrecursive Equivalent of the Conjugate Gradient Method without the Need to Restart |
| title_full_unstemmed | Nonrecursive Equivalent of the Conjugate Gradient Method without the Need to Restart |
| title_short | Nonrecursive Equivalent of the Conjugate Gradient Method without the Need to Restart |
| title_sort | nonrecursive equivalent of the conjugate gradient method without the need to restart |
| url | http://dx.doi.org/10.1155/2019/7527590 |
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