Geometric integration on manifold of square oblique rotation matrices

SIAM Journal on Matrix Analysis and Applications

Volumn 23, Issue 4, 2002, Pages 974-989

  Del Buono, N ^a   Lopez, L ^a  

^a UNIVERSITY OF BARI   (Italy)

Author keywords

Condition number function; Manifolds; Oblique Procrustes problems; Runge Kutta methods; Square oblique rotation matrices

Indexed keywords

EID: 0036399140     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S089547980037768X     Document Type: Article

References (23)

1. M.W. Browne, Oblique rotation to a partially specified target, British J. Math. Statist. Psych., 25 (1972), pp. 207-212.
2. M.P. Calvo, A. Iserles, and A. Zanna, Numerical solution of isospectral flows, Math. Comp., 66 (1997), pp. 1461-1486.
3. M.T. Chu, A list of matrix flows with applications, in Hamiltonian and Gradient Flows, Algorithms and Control, Fields Inst. Commun. 3, AMS, Providence, RI, 1994, pp. 87-97.
4. M.T. Chu, Scaled Toda-like flows, Linear Algebra Appl., 215 (1995), pp. 261-273.
5. n-1 that lead to eigenvalues or their means of a matrix, SIAM J. Alg. Disc. Meth., 7 (1986), pp. 425-432.
6. G. Cooper, Stability of Runge-Kutta methods for trajectory problems, IMA J. Numer. Anal., 7 (1987), pp. 1-13.
7. T.F. Cox and M.A.A. Cox, Multidimensional Scaling, Chapman & Hall, London, 1995.
8. L. Dieci, D. Russell, and E. Van Vleck, Unitary integrators and applications to continuous orthonormalization techniques, SIAM J. Numer. Anal., 31 (1994), pp. 261-281.
9. F. Diele, L. Lopez, and R. Peluso, The Cayley transform in the numerical solution of unitary differential systems, Adv. Comput. Math., 8 (1998), pp. 317-334.
10. T. Eirola and J.M. Sanz-Serna, Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods, Numer. Math., 61 (1992), pp. 281-290.
11. G.H. Golub and C.F. Van Loan, Matrix Computations, Johns Hopkins University Press, Baltimore, 1983.
12. J.C. Gower, Multivariate analysis: Ordination, multidimensional scaling and allied topics, in Handbook of Applicable Mathematics, Vol. IV: Statistics, Part B, E. Lloyd, ed., John Wiley & Sons, New York, 1984, pp. 727-781.
13. G.T. Gruvaeus, A general approach to Procrustes pattern rotation, Psychometrika, 35 (1970), pp. 493-505.
14. E. Hairer, S.P. Norsett, and G. Wanner, Solving Ordinary Differential Equations, Vol. I: Nonstiff Problems, 2nd ed., Springer-Verlag, Berlin, 1991.
15. E. Hairer and G. Wanner, Solving Ordinary Differential Equations, Vol. II, Springer-Verlag, Berlin, 1991.
16. A. Iserles, H. Munte-Kaas, S.P. Nopsett, and A. Zanna, Lie group methods, in Acta Numerica 9, Cambridge University Press, Cambridge, UK, 2000, pp. 215-365.
17. H.A.L. Kiers, Joint orthomax rotation of the core and component matrices resulting from a three-mode factor analysis, J. Classification, 15 (1998), pp. 245-263.
18. S.A. Mulaik, The Foundations of Factor Analysis, McGraw-Hill, New York, 1972.
19. J.M. Sanz-Serna and M.P. Calvo, Numerical Hamiltonian Problems, Chapman & Hall, London, 1994.
20. A.M. Stuart and A.R. Humphries, Dynamical Systems and Numerical Analysis, Cambridge University Press, Cambridge, UK, 1996.
21. N.T. Trendafilov, A continuous-time approach to the oblique Procrustes problem, Behaviormetrika, 26 (1999), pp. 167-181.
22. N.T. Trendafilov and R.A. Lippert, The multimode Procrustes problem, Linear Algebra Appl., to appear.
23. H.K. Wilson, Ordinary Differential Equations, Addison-Wesley, London, 1971.