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关于解极大相关问题P-SOR算法的收敛性 被引量：3

ON THE CONVERGENCE OF THE P-SOR METHOD FOR SOLVING MAXIMAL CORRELATION PROBLEM
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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. This paper concentrates on the convergence of the P-SOR algorithm for maximal cor- relation 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 w 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.
作者 秦晓伟 刘新国 赵娜
机构地区 中国海洋大学数学科学学院
出处 《计算数学》 CSCD 北大核心 2011年第4期345-356,共12页 Mathematica Numerica Sinica
基金 国家自然科学基金(10971204 11071228) 国家科技重大专项(2008ZX05025-001-006)部分资助
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 Canonical correlation analysis Maximal correlation problem Multivariate eigenvalue problem P-SOR algorithm the relaxation parameter starting point strategy convergence
分类号 O241.6 [理学—计算数学]
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参考文献12

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  • 2Hotelling H. Relations between two sets of variates[J]. Biometrika, 1936, 28, 321-377.
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共引文献1

同被引文献42

  • 1李成林,宋莎莎,韩振南.基于nCode Design-Life的某车架疲劳可靠性分析[J].图学学报,2014,35(1):42-45. 被引量：54
  • 2王同科,谷同祥.Poisson方程差分格式的SOR方法中最优松弛因子的回归分析方法[J].工程数学学报,2005,22(3):474-480. 被引量：6
  • 3Hotelling H. The most predictable criterion [J]. J Educ Pyschol,1935, 26: 139-142.
  • 4Hotelling H. Relations between two sets of variates [J]. Biometri- ka,1936, 28: 321-377.
  • 5Chu MT, Watterson J L. On a multivariate eigenvalue problem, Part I.. Algebraic theory and a power method [J]. SIAM J Sci Comput, 1993(14): 1089-1106.
  • 6HorstP. Relations among m sets of measures [J]. Psychometrika, 1961, 26: 129-149.
  • 7Hu D K. The convergence property of a algorithm about general- ized eigenvalue and eigenvector of positive definite matrix [C]. Bei- jing: China-Japan Symposium on Statistics, 1984.
  • 8孙继广.多参数特征值问题的一种算法[J].计算数学,1986,8(2):137-149.
  • 9Hanafi M, Ten Berge J M F. Global optimality of the successive Maxbet algorithm [J]. Psychometrika; 2003(68) : 97-103.
  • 10Zhang L H, Liao L Z. An alternating variable method for the max- imal correlation problem [J]. J Global Optim, DOI: 10. 1007/s 10898-011-9758-2.

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计算数学
2011年 第4期

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