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Setting up alternating least squares and iterative majorization algorithms for solving various matrix optimization problems


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  • Kiers, Henk A. L.
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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 41 (2002)
    Issue (Month): 1 (November)
    Pages: 157-170

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    Handle: RePEc:eee:csdana:v:41:y:2002:i:1:p:157-170

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    1. Henk Kiers, 1995. "Maximization of sums of quotients of quadratic forms and some generalizations," Psychometrika, Springer, vol. 60(2), pages 221-245, June.
    2. Norman Cliff, 1966. "Orthogonal rotation to congruence," Psychometrika, Springer, vol. 31(1), pages 33-42, March.
    3. Henk Kiers & Jos Berge, 1992. "Minimization of a class of matrix trace functions by means of refined majorization," Psychometrika, Springer, vol. 57(3), pages 371-382, September.
    4. Jan Leeuw, 1988. "Convergence of the majorization method for multidimensional scaling," Journal of Classification, Springer, vol. 5(2), pages 163-180, September.
    5. Henk Kiers, 1990. "Majorization as a tool for optimizing a class of matrix functions," Psychometrika, Springer, vol. 55(3), pages 417-428, September.
    6. Jos Berge & Klaas Nevels, 1977. "A general solution to Mosier's oblique procrustes problem," Psychometrika, Springer, vol. 42(4), pages 593-600, December.
    7. Henk Kiers, 1997. "Weighted least squares fitting using ordinary least squares algorithms," Psychometrika, Springer, vol. 62(2), pages 251-266, June.
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    Cited by:
    1. Raoul Pietersz & Patrick J. F. Groenen, 2005. "Rank Reduction of Correlation Matrices by Majorization," Finance, EconWPA 0502006, EconWPA.
    2. Qingna Li & Houduo Qi & Naihua Xiu, 2011. "Block relaxation and majorization methods for the nearest correlation matrix with factor structure," Computational Optimization and Applications, Springer, vol. 50(2), pages 327-349, October.
    3. Kuroda, Masahiro & Mori, Yuichi & Iizuka, Masaya & Sakakihara, Michio, 2011. "Acceleration of the alternating least squares algorithm for principal components analysis," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 55(1), pages 143-153, January.


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