| 求张量扩展特征值的幂法 |
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| 引用本文： | 王佳佳,胡毅庆,赵金玲,徐尔. 求张量扩展特征值的幂法[J]. 井冈山大学学报(自然科学版), 2015, 0(6): 12-16 |
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| 作者姓名： | 王佳佳 胡毅庆 赵金玲 徐尔 |
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| 作者单位： | 北京科技大学数理学院, 北京 100083,北京科技大学数理学院, 北京 100083,北京科技大学数理学院, 北京 100083,北京科技大学数理学院, 北京 100083 |
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| 基金项目： | 国家自然科学基金青年基金项目(11101028);北京高校青年英才计划项目(YETP0385) |
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| 摘 要： | 针对与牛顿迭代相关的张量扩展特征值问题,在对已有张量特征值和幂法的研究基础上,提出了求解与牛顿迭代有关的张量扩展特征值和特征向量的幂法,分析了该幂法的收敛性。最后数值试验结果验证了该幂法的有效性。
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| 关 键 词： | 牛顿法 张量 特征值 幂法 收敛性 |
| 收稿时间： | 2015-08-09 |
| 修稿时间： | 2015-09-12 |
POWER METHOD FOR COMPUTING EXTENSION EIGENVALUES OF TENSOR |
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| WANG Jia-ji,HU Yi-qing,ZHAO Jin-ling and XU Er. POWER METHOD FOR COMPUTING EXTENSION EIGENVALUES OF TENSOR[J]. Journal of Jinggangshan University(Natural Sciences Edition), 2015, 0(6): 12-16 |
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| Authors: | WANG Jia-ji HU Yi-qing ZHAO Jin-ling XU Er |
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| Affiliation: | School of Mathematics and Physics, University of Science & Technology Beijing, Beijing 100083, China,School of Mathematics and Physics, University of Science & Technology Beijing, Beijing 100083, China,School of Mathematics and Physics, University of Science & Technology Beijing, Beijing 100083, China and School of Mathematics and Physics, University of Science & Technology Beijing, Beijing 100083, China |
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| Abstract: | Tensor eigenvalue problem associated with the Newton iteration method was studied in this paper. Based on the research of tensor eigenvalues and power method, we firstly presented the power method that solved the extension eigenvalue and corresponding eigenvector of tensor. Furthermore, the convergence of the power method was proved. Finally, numerical results have shown that the method is effective. |
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| Keywords: | Newton's method tensor eigenvalue power method convergence |
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