| 关于解极大相关问题P-SOR算法的收敛性 |
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| 引用本文： | 秦晓伟,刘新国,赵娜. 关于解极大相关问题P-SOR算法的收敛性[J]. 计算数学, 2011, 33(4): 345-356 |
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| 作者姓名： | 秦晓伟 刘新国 赵娜 |
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| 作者单位： | 中国海洋大学数学科学学院, 山东青岛 266100 |
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| 基金项目： | 国家自然科学基金，国家科技重大专项(2008ZX05025-001-006)部分资助 |
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| 摘 要： | 对求解极大相关问题的P-SOR方法的收敛性做了进一步研究.得到了一些新的收敛条件.为了提高收敛到全局最大解的可能性,提出了一种新的初始向量选择策略.给出了P-SOR算法的对称形式(P-SSOR).还给出了一种算法精化策略.最后,用数值例子说明新方法的有效性.
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| 关 键 词： | 典型相关分析 极大相关问题 多元特征值问题 P-SOR算法,松弛因子 初始点策略 收敛性 |
| 收稿时间： | 2010-08-12; |
ON THE CONVERGENCE OF THE P-SOR METHOD FOR SOLVING MAXIMAL CORRELATION PROBLEM |
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| Qin Xiaowei,Liu Xinguo,Zhao Na. ON THE CONVERGENCE OF THE P-SOR METHOD FOR SOLVING MAXIMAL CORRELATION PROBLEM[J]. Mathematica Numerica Sinica, 2011, 33(4): 345-356 |
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| Authors: | Qin Xiaowei Liu Xinguo Zhao Na |
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| Affiliation: | School of Mathematical Sciences, Ocean University of China, Qingdao 266100, Shandong, China |
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| Abstract: | This paper concentrates on the convergence of the P-SOR algorithm for maximal correlation problems (MCP) proposed by Sun and contains four contributions. Several new results on the convergence of the P-SOR method are obtained. To increase the probability of finding a global maximizer, a new staring point strategy is proposed. A so-called P-SSOR algorithm is presented and shown that the new algorithm is less sensitive to the selection of the relaxation parameter ω than P-SOR algorithm. Finally, a refining strategy to compute the global maximizer is suggested. Some numerical examples are carried out to demonstrate the efficiency of the new algorithm with the new starting point strategy. |
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| Keywords: | Canonical correlation analysis Maximal correlation problem Multivariate eigenvalue problem P-SOR algorithm the relaxation parameter starting point strategy convergence |
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