On a differential equation approach to the weighted orthogonal Procrustes problem

Statistics and Computing

Volumn 8, Issue 2, 1998, Pages 125-133

  Chu, Moody T ^a   Trendafilov, Nickolay T ^b,c  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

^b INSTITUTE OF MATHEMATICS AND INFORMATICS   (Bulgaria)

^c UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

Constrained regression; Optimality condition; Procrustes rotation; Projected gradient

Indexed keywords

EID: 0042725448     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008934100736     Document Type: Article

References (17)

1. Bellman, R. (1970) Introduction to Matrix Analysis. 2nd edn. New York: McGraw-Hill.
2. Chu, M. T. (1994) A list of matrix flows with applications. Fields Institute Communications, 3, 87-97.
3. Chu, M. T. and Driessel, K. R. (1990) The projected gradient method for least squares matrix approximations with spectral constraints. SIAM Journal of Numerical Analysis, 27, 1050-60.
4. Chu, M. T. and Trendafilov, N. (1996) The orthogonally constrained regression revisited. Submitted for publication.
5. Gear, C. W. (1986) Maintaining solution invariants in the numerical solution of ODEs. SIAM Journal of Sci. Stat. Comput., 7, 734-43.
6. Gill, P. E., Murray, W. and Wright, M. H. (1981) Practical Optimization. Florida: Academic Press.
7. Golub, G. H. and Van Loan, C. F. (1991) Matrix Computation. 2nd edn. Baltimore: The Johns Hopkins University Press.
8. Gower, J. C. (1984) Multivariate analysis: Ordination, multidimensional scaling and allied topics. In Emlyn Lloyd (ed.) Handbook of Applicable Mathematics, Volume IV: Statistics, part B. New York: John Wiley & Sons.
9. Guillemin, V. and Pollack, A. (1974) Differential Topology. New Jersey: Prentice-Hall Inc.
10. Helmke, U. and Moore, J. B. (1994) Optimization and Dynamical Systems. London: Springer Verlag.
11. Hirsch, M. W. and Smale, S. (1974) Differential Equations, Dynamical Systems, and Linear Algebra. London: Academic Press.
12. Koschat, M. A. and Swayne, D. F. (1991) A weighted Procrustes criterion. Psychometrika, 56, 229-39.
13. Mooijaart, A. and Commandeur, J. J. F. (1990) A general solution of the weighted orthonormal Procrustes problem. Psychometrika, 55, 657-63.
14. Mulaik, S. A. (1972) The Foundations of Factor Analysis. New York: McGraw-Hill.
15. Ortega, J. and Rheinboldt, W. (1970) Iterative Solutions of Non-linear Equations in Several Variables. London: Academic Press.
16. Shampine, L. F. and Reichelt, M. W. (1997) The MATLAB ODE suite. SIAM Journal on Scientific Computing, 18, 1-22.
17. ten Berge, J. M. F. (1977) Orthogonal Procrustes rotation for two or more matrices. Psychometrika, 42, 267-76.