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A multigrid method for the maximal correlation problem
| 1. | School of Mathematical Science, Ocean University of China, Qiaodao 266100, China, China |
References:
| [1] |
M. T. Chu and J. L. Watterson, On a multivariate eigenvalue problem, Part I: Algebraic theory and a power method, SIAM J. Sci. Comput., 14 (1993), 1089-1106.
doi: 10.1137/0914066. |
| [2] |
M. Y. Fu, Z. Q. Luo and Y. Y. Ye, Approximation algorithms for quadratic programming, J. Comb. Optim., 2 (1998), 29-50.
doi: 10.1023/A:1009739827008. |
| [3] |
G. H. Golub and C. F. Van Loan, "Matrix Computations," Third Edition, The Johns Hopkins University Press, Baltimore, 1996. |
| [4] |
S. M. Grzegórski, On the convergence of the method of alternating projections for multivariate symmetric eigenvalue problem, Numan 2010, Conference in Numerical Analysis, Chania, Greece, Sept 15-18, 2010. |
| [5] |
W. Hackbusch, "Multi-grid Method and Applications," Springer-Verlag, New York, 1985. |
| [6] |
M. Hanafi and J. M. F. Ten Berge, Global optimality of the successive Maxbet algorithm, Psychometrika, 68 (2003), 97-103.
doi: 10.1007/BF02296655. |
| [7] |
P. Horst, Relations among m sets of measures, Psychometrika, 26 (1961), 129-149.
doi: 10.1007/BF02289710. |
| [8] |
D.-K. Hu, The convergence property of a algorithm about generalized eigenvalue and eigenvector of positive definite matrix, China-Japan Symposium on Statistics, 1984, Beijing, China. |
| [9] |
J. R. Kettenring, Canonical analysis of several sets of variables, Biometrika, 58 (1971), 433-451.
doi: 10.1093/biomet/58.3.433. |
| [10] |
Z.-Y. Liu, J. Qian and S.-F. Xu, On the double eigenvalue problem, preprint. Available online: http://www.math.pku.edu.cn:8000/var/preprint/7229.pdf. |
| [11] |
J.-G. Sun, An algorithm for the solution of multiparameter eigenvalue problem, Math. Numer. Sinica(Chinese), 8 (1986), 137-149. |
| [12] |
J. M. F. Ten Berge, Generalized approaches to the MAXBET problem and the MAXDIFF problem, with applications to canonical correlations, Psychometrika, 53 (1988), 487-494.
doi: 10.1007/BF02294402. |
| [13] |
T. L. Van Noorden and J. Barkmeijer, The multivariate eigenvalue problem: A new application, theory and a subspace accelerated power method, Universiteit Utrecht, preprint, 2008. Available online: http://www.math.uu.nl/publications/preprints/1308.ps |
| [14] |
L.-H. Xu, "Numerical Methods for the Multivariate Eigenvalue Problem," M.S. Thesis, Department of Mathematics, Ocean University of China, 2008, ( in Chinese). Available from: http://cdmd.cnki.com.cn/Article/CDMD-10423-2008175406.htm |
| [15] |
S.-F. Xu, "Matrix Computations: Theory and Methods," Peking University Press, Bejing, 1995 (Chinese). |
| [16] |
Y. Y. Ye, Approximating quadratic programming with bound and quadratic constraints, Math. Program., 84 (1999), 219-226.
doi: 10.1007/s10107980012a. |
| [17] |
L.-H. Zhang and M. T. Chu, Computing absolute maximum correlation, IMA J. Numer. Anal., 32 (2012), 163-184.
doi: 10.1093/imanum/drq029. |
| [18] |
L.-H. Zhang and L.-Z. Liao, An alternating variable method for the maximal correlation problem, J. Global Optim., 54 (2012), 199-218.
doi: 10.1007/s10898-011-9758-2. |
| [19] |
L.-H. Zhang, L.-Z. Liao and L.-M. Sun, Towards the global solution of the maximal correlation problem, J. Global Optim., 49 (2011), 91-107.
doi: 10.1007/s10898-010-9536-6. |
| [20] |
L. Zhang, Y. Xu and Z. Jin, An efficient algorithm for convex quadratic semi-definite optimization, Numer. Algebra Control Optim., 2 (2012), 129-144.
doi: 10.3934/naco.2012.2.129. |
show all references
References:
| [1] |
M. T. Chu and J. L. Watterson, On a multivariate eigenvalue problem, Part I: Algebraic theory and a power method, SIAM J. Sci. Comput., 14 (1993), 1089-1106.
doi: 10.1137/0914066. |
| [2] |
M. Y. Fu, Z. Q. Luo and Y. Y. Ye, Approximation algorithms for quadratic programming, J. Comb. Optim., 2 (1998), 29-50.
doi: 10.1023/A:1009739827008. |
| [3] |
G. H. Golub and C. F. Van Loan, "Matrix Computations," Third Edition, The Johns Hopkins University Press, Baltimore, 1996. |
| [4] |
S. M. Grzegórski, On the convergence of the method of alternating projections for multivariate symmetric eigenvalue problem, Numan 2010, Conference in Numerical Analysis, Chania, Greece, Sept 15-18, 2010. |
| [5] |
W. Hackbusch, "Multi-grid Method and Applications," Springer-Verlag, New York, 1985. |
| [6] |
M. Hanafi and J. M. F. Ten Berge, Global optimality of the successive Maxbet algorithm, Psychometrika, 68 (2003), 97-103.
doi: 10.1007/BF02296655. |
| [7] |
P. Horst, Relations among m sets of measures, Psychometrika, 26 (1961), 129-149.
doi: 10.1007/BF02289710. |
| [8] |
D.-K. Hu, The convergence property of a algorithm about generalized eigenvalue and eigenvector of positive definite matrix, China-Japan Symposium on Statistics, 1984, Beijing, China. |
| [9] |
J. R. Kettenring, Canonical analysis of several sets of variables, Biometrika, 58 (1971), 433-451.
doi: 10.1093/biomet/58.3.433. |
| [10] |
Z.-Y. Liu, J. Qian and S.-F. Xu, On the double eigenvalue problem, preprint. Available online: http://www.math.pku.edu.cn:8000/var/preprint/7229.pdf. |
| [11] |
J.-G. Sun, An algorithm for the solution of multiparameter eigenvalue problem, Math. Numer. Sinica(Chinese), 8 (1986), 137-149. |
| [12] |
J. M. F. Ten Berge, Generalized approaches to the MAXBET problem and the MAXDIFF problem, with applications to canonical correlations, Psychometrika, 53 (1988), 487-494.
doi: 10.1007/BF02294402. |
| [13] |
T. L. Van Noorden and J. Barkmeijer, The multivariate eigenvalue problem: A new application, theory and a subspace accelerated power method, Universiteit Utrecht, preprint, 2008. Available online: http://www.math.uu.nl/publications/preprints/1308.ps |
| [14] |
L.-H. Xu, "Numerical Methods for the Multivariate Eigenvalue Problem," M.S. Thesis, Department of Mathematics, Ocean University of China, 2008, ( in Chinese). Available from: http://cdmd.cnki.com.cn/Article/CDMD-10423-2008175406.htm |
| [15] |
S.-F. Xu, "Matrix Computations: Theory and Methods," Peking University Press, Bejing, 1995 (Chinese). |
| [16] |
Y. Y. Ye, Approximating quadratic programming with bound and quadratic constraints, Math. Program., 84 (1999), 219-226.
doi: 10.1007/s10107980012a. |
| [17] |
L.-H. Zhang and M. T. Chu, Computing absolute maximum correlation, IMA J. Numer. Anal., 32 (2012), 163-184.
doi: 10.1093/imanum/drq029. |
| [18] |
L.-H. Zhang and L.-Z. Liao, An alternating variable method for the maximal correlation problem, J. Global Optim., 54 (2012), 199-218.
doi: 10.1007/s10898-011-9758-2. |
| [19] |
L.-H. Zhang, L.-Z. Liao and L.-M. Sun, Towards the global solution of the maximal correlation problem, J. Global Optim., 49 (2011), 91-107.
doi: 10.1007/s10898-010-9536-6. |
| [20] |
L. Zhang, Y. Xu and Z. Jin, An efficient algorithm for convex quadratic semi-definite optimization, Numer. Algebra Control Optim., 2 (2012), 129-144.
doi: 10.3934/naco.2012.2.129. |
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