A Prediction-Correction Dynamic Method for Large-Scale Generalized Eigenvalue Problems
This paper gives a new prediction-correction method based on the dynamical system of differential-algebraic equations for the smallest generalized eigenvalue problem. First, the smallest generalized eigenvalue problem is converted into an equivalent-constrained optimization problem. Second, accordin...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/845459 |
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| _version_ | 1832563697190436864 |
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| author | Xin-long Luo Jia-ru Lin Wei-ling Wu |
| author_facet | Xin-long Luo Jia-ru Lin Wei-ling Wu |
| author_sort | Xin-long Luo |
| collection | DOAJ |
| description | This paper gives a new prediction-correction method based on the dynamical system of differential-algebraic equations for the smallest generalized eigenvalue problem. First, the smallest generalized eigenvalue problem is converted into an equivalent-constrained optimization problem. Second, according to the Karush-Kuhn-Tucker conditions of this special equality-constrained problem, a special continuous dynamical system of differential-algebraic equations is obtained. Third, based on the implicit Euler method and an analogous trust-region technique, a prediction-correction method is constructed to follow this system of differential-algebraic equations to compute its steady-state solution. Consequently, the smallest generalized eigenvalue of the original problem is obtained. The local superlinear convergence property for this new algorithm is also established. Finally, in comparison with other methods, some promising numerical experiments are presented. |
| format | Article |
| id | doaj-art-389fea40cad548548693175b7cd7ead2 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-389fea40cad548548693175b7cd7ead22025-02-03T01:12:52ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/845459845459A Prediction-Correction Dynamic Method for Large-Scale Generalized Eigenvalue ProblemsXin-long Luo0Jia-ru Lin1Wei-ling Wu2School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, P.O. Box 101, Beijing 100876, ChinaSchool of Information and Communication Engineering, Beijing University of Posts and Telecommunications, P.O. Box 101, Beijing 100876, ChinaSchool of Information and Communication Engineering, Beijing University of Posts and Telecommunications, P.O. Box 101, Beijing 100876, ChinaThis paper gives a new prediction-correction method based on the dynamical system of differential-algebraic equations for the smallest generalized eigenvalue problem. First, the smallest generalized eigenvalue problem is converted into an equivalent-constrained optimization problem. Second, according to the Karush-Kuhn-Tucker conditions of this special equality-constrained problem, a special continuous dynamical system of differential-algebraic equations is obtained. Third, based on the implicit Euler method and an analogous trust-region technique, a prediction-correction method is constructed to follow this system of differential-algebraic equations to compute its steady-state solution. Consequently, the smallest generalized eigenvalue of the original problem is obtained. The local superlinear convergence property for this new algorithm is also established. Finally, in comparison with other methods, some promising numerical experiments are presented.http://dx.doi.org/10.1155/2013/845459 |
| spellingShingle | Xin-long Luo Jia-ru Lin Wei-ling Wu A Prediction-Correction Dynamic Method for Large-Scale Generalized Eigenvalue Problems Abstract and Applied Analysis |
| title | A Prediction-Correction Dynamic Method for Large-Scale Generalized Eigenvalue Problems |
| title_full | A Prediction-Correction Dynamic Method for Large-Scale Generalized Eigenvalue Problems |
| title_fullStr | A Prediction-Correction Dynamic Method for Large-Scale Generalized Eigenvalue Problems |
| title_full_unstemmed | A Prediction-Correction Dynamic Method for Large-Scale Generalized Eigenvalue Problems |
| title_short | A Prediction-Correction Dynamic Method for Large-Scale Generalized Eigenvalue Problems |
| title_sort | prediction correction dynamic method for large scale generalized eigenvalue problems |
| url | http://dx.doi.org/10.1155/2013/845459 |
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