Gradient flows and double bracket equations

Differential Geometry and its Application

Volumn 20, Issue 2, 2004, Pages 209-224

  Tam, Tin Yau ^a  

^a AUBURN UNIVERSITY   (United States)

Author keywords

Double bracket equations; Gradient flows; Least squares optimizations; Orthogonal projections; Reduction groups

Indexed keywords

EID: 1142303123     PISSN: 09262245     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.difgeo.2003.10.008     Document Type: Article

References (16)

1. Bott R. On torsion in Lie groups Proc. Nat. Acad. Sci. USA 40 1954 586-588
2. Bloch A.M. Brockett R.W. Ratiu T. Completely integrable gradient flows Comm. Math. Phys. 147 1992 57-74
3. Brockett R.W. Dynamical system that sort lists, diagonalize matrices and solving least squares programming problems Linear Algebra Appl. 146 1991 79-91
4. Brockett R.W. Differential geometry and the design of gradient algorithms Proc. Symp. Pure Math. 54 I 1993 69-92
5. Chu M.T. Constructing a Hermitian matrix from its diagonal entries and eigenvalues SIAM J. Matrix Anal. Appl. 16 1995 207-217
6. Chu M.T. Inverse eigenvalue problems SIAM Rev. 40 1998 1-39
7. Chu M.T. Driessel K. The projected gradient method for least squares matrix approximations with spectral constraints SIAM J. Numer. Anal. 27 1990 1050-1060
8. Duistermaat J.J. Kolk J.A.C. Varadarajan V.S. Functions, flows and oscillatory integrals on flag manifolds and conjugacy classes in real semisimple Lie groups Compositio Math. 49 1983 309-398
9. Helgason S. Differential Geometry, Lie Groups and Symmetric Spaces 1978 Academic Press San Diego, CA
10. Holmes R.R. Tam T.Y. Distance to the convex hull of an orbit under the action of a compact Lie group J. Austral. Math. Soc. Ser. A 66 1999 331-357
11. Hunt G.A. A theorem of Élie Cartan Proc. Amer. Math. Soc. 7 1956 307-308
12. Knapp A.W. Lie Groups Beyond an Introduction 1996 Birkhäuser Boston
13. Kostant B. On convexity, the Weyl group and Iwasawa decomposition Ann. Sci. Ecole Norm. Sup. (4) 6 1973 413-460
14. Tam T.Y. An extension of a result of Lewis Electronic J. Linear Algebra 5 1999 1-10
15. Varadarajan V.S. The method of stationary phase and applications to geometry and analysis on Lie groups In: Orsted B. Schlichtkrull H. (Eds.), Algebraic and Analytic Methods in Representation Theory, Perspectives in Mathematics vol. 17 1997 167-242 Academic Press
16. Vogan D.A.Jr. The method of stationary phase and applications to geometry and analysis on Lie groups Orsted B. Schlichtkrull H. Algebraic and Analytic Methods in Representation Theory, Perspectives in Mathematics vol. 17 1997 243-339 Academic Press