User menu

Intrinsic representation of tangent vectors and vector transport on matrix manifolds

Bibliographic reference Huang, Wen ; Absil, Pierre-Antoine ; Gallivan, Kyle A.. Intrinsic representation of tangent vectors and vector transport on matrix manifolds. In: Numerische Mathematik, , p. 1-21 (October 27, 2016)
Permanent URL http://hdl.handle.net/2078.1/179397
  1. Anderson E., Bai Z., Bischof C., Blackford L. S., Demmel J., Dongarra J., Du Croz J., Greenbaum A., Hammarling S., McKenney A., Sorensen D., LAPACK Users' Guide, ISBN:9780898714470, 10.1137/1.9780898719604
  2. Absil P.-A., Baker C.G., Gallivan K.A., Trust-Region Methods on Riemannian Manifolds, 10.1007/s10208-005-0179-9
  3. Adler R. L., Newton's method on Riemannian manifolds and a geometric model for the human spine, 10.1093/imanum/22.3.359
  4. Absil, P.-A., Mahony, R., Sepulchre, R.: Optimization algorithms on matrix manifolds. Princeton University Press, Princeton, NJ (2008)
  5. Absil P.-A., Oseledets I. V., Low-rank retractions: a survey and new results, 10.1007/s10589-014-9714-4
  6. Afsari Bijan, Tron Roberto, Vidal René, On the Convergence of Gradient Descent for Finding the Riemannian Center of Mass, 10.1137/12086282x
  7. Boumal, N., Absil, P.A.: RTRMC: A Riemannian trust-region method for low-rank matrix completion. Adv. Neural Inf. Process. Syst. 24(NIPS), 406–414 (2011)
  8. Bini Dario A., Iannazzo Bruno, Computing the Karcher mean of symmetric positive definite matrices, 10.1016/j.laa.2011.08.052
  9. Boothby, W.M.: An introduction to differentiable manifolds and Riemannian geometry, 2nd edn. Academic Press, USA (1986)
  10. Dai Wei, Kerman Ely, Milenkovic Olgica, A Geometric Approach to Low-Rank Matrix Completion, 10.1109/tit.2011.2171521
  11. Edelman Alan, Arias Tomás A., Smith Steven T., The Geometry of Algorithms with Orthogonality Constraints, 10.1137/s0895479895290954
  12. Golub, G.H., Van Loan, C.F.: Matrix computations. Johns Hopkins Studies in the Mathematical Sciences, 3rd edn. Johns Hopkins University Press, USA (1996)
  13. Goemans Michel X., Williamson David P., Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming, 10.1145/227683.227684
  14. Huang Wen, Absil P.-A., Gallivan K. A., A Riemannian symmetric rank-one trust-region method, 10.1007/s10107-014-0765-1
  15. Huang Wen, Absil P.-A., Gallivan Kyle A., A Riemannian BFGS Method for Nonconvex Optimization Problems, Lecture Notes in Computational Science and Engineering (2016) ISBN:9783319399270 p.627-634, 10.1007/978-3-319-39929-4_60
  16. Huang Wen, Gallivan K. A., Absil P.-A., A Broyden Class of Quasi-Newton Methods for Riemannian Optimization, 10.1137/140955483
  17. Huang Wen, Gallivan Kyle A., Srivastava Anuj, Absil Pierre-Antoine, Riemannian Optimization for Registration of Curves in Elastic Shape Analysis, 10.1007/s10851-015-0606-8
  18. Huang Wen, Gallivan Kyle A., Zhang Xiangxiong, Solving PhaseLift by Low-rank Riemannian Optimization Methods 1, 10.1016/j.procs.2016.05.422
  19. Kleinsteuber Martin, Shen Hao, Blind Source Separation With Compressively Sensed Linear Mixtures, 10.1109/lsp.2011.2181945
  20. Series Editors, Profiles of Drug Substances, Excipients and Related Methodology (2011) ISBN:9780123876676 p.ii, 10.1016/b978-0-12-387667-6.00013-0
  21. Mishra B., Meyer G., Sepulchre R., Low-rank optimization for distance matrix completion, 10.1109/cdc.2011.6160810
  22. Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd ed. Springer, New York (2006)
  23. Qi, C., Gallivan, K.A., Absil, P.-A.: Riemannian BFGS algorithm with applications. Recent Advances in Optimization and its Applications in Engineering, pp. 183–192 (2010)
  24. Ring Wolfgang, Wirth Benedikt, Optimization Methods on Riemannian Manifolds and Their Application to Shape Space, 10.1137/11082885x
  25. Selvan S. E., Amato U., Gallivan K. A., Chunhong Qi, Carfora M. F., Larobina M., Alfano B., Descent Algorithms on Oblique Manifold for Source-Adaptive ICA Contrast, 10.1109/tnnls.2012.2218060
  26. Sander Oliver, Geodesic finite elements for Cosserat rods, 10.1002/nme.2814
  27. Sato, H.: A Dai-Yuan-type Riemannian conjugate gradient method with the weak Wolfe conditions. Comput. Optim. Appl. (2015) (to appear)
  28. Sato Hiroyuki, Iwai Toshihiro, A new, globally convergent Riemannian conjugate gradient method, 10.1080/02331934.2013.836650
  29. Turaga P., Veeraraghavan A., Srivastava A., Chellappa R., Statistical Computations on Grassmann and Stiefel Manifolds for Image and Video-Based Recognition, 10.1109/tpami.2011.52
  30. Vandereycken Bart, Low-Rank Matrix Completion by Riemannian Optimization, 10.1137/110845768
  31. Vandereycken Bart, Absil P.-A., Vandewalle Stefan, Embedded geometry of the set of symmetric positive semidefinite matrices of fixed rank, 10.1109/ssp.2009.5278558