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A Gradient-Descent Method for Curve Fitting on Riemannian Manifolds

  1. Absil P.-A., Gallivan K. A., Accelerated Line-search and Trust-region Methods, 10.1137/08072019x
  2. Absil P. A., Mahony R., Andrews B., Convergence of the Iterates of Descent Methods for Analytic Cost Functions, 10.1137/040605266
  3. Absil P.-A., Mahony R., Sepulchre R., Optimization Algorithms on Matrix Manifolds : , ISBN:9781400830244, 10.1515/9781400830244
  4. P.A. Absil, J. Trumpf, R. Mahony, B. Andrews, All roads lead to Newton: feasible second-order methods for equality-constrained optimization, Technical report UCL-INMA-2009.024 (2009).
  5. Altafini Claudio, The de casteljau algorithm on SE(3), Nonlinear control in the Year 2000 ISBN:9781852333638 p.23-34, 10.1007/bfb0110205
  6. D.P. Bertsekas, Nonlinear Programming (Athena Scientific, Belmont, 1995).
  7. W.M. Boothby, An Introduction to Differentiable Manifolds and Riemannian Geometry, revised 2nd edn. (Academic Press, San Diego, 2003).
  8. CAMARINHA M., SILVA LEITE F., CROUCH P., Splines of class Ck on non-euclidean spaces, 10.1093/imamci/12.4.399
  9. Carmo Manfredo Perdigão do, Riemannian Geometry, ISBN:9780817634902, 10.1007/978-1-4757-2201-7
  10. Chavel Isaac, Riemannian Geometry : A Modern Introduction, ISBN:9780511616822, 10.1017/cbo9780511616822
  11. Crouch P., Kun G., Leite F. Silva, 10.1023/a:1021770717822
  12. P. Crouch, F. Silva Leite, Geometry and the dynamic interpolation problem, in Proc. Am. Control Conf. (Boston, 26–29 July, 1991), pp. 1131–1136.
  13. Crouch P., Leite F. Silva, The dynamic interpolation problem: On Riemannian manifolds, Lie groups, and symmetric spaces, 10.1007/bf02254638
  14. N. Dyn, Linear and nonlinear subdivision schemes in geometric modeling, in Foundations of Computational Mathematics, Hong Kong, 2008. London Math. Soc. Lecture Note Ser., vol. 363 (Cambridge University Press Cambridge, 2009), pp. 68–92.
  15. Gallot Sylvestre, Hulin Dominique, Lafontaine Jacques, Riemannian Geometry, ISBN:9783540204930, 10.1007/978-3-642-18855-8
  16. Hüper K., Silva Leite F., On the Geometry of Rolling and Interpolation Curves on S n , SO n , and Grassmann Manifolds, 10.1007/s10883-007-9027-3
  17. Jakubiak Janusz, Silva Leite Fátima, Rodrigues Rui C., A two-step algorithm of smooth spline generation on Riemannian manifolds, 10.1016/j.cam.2005.07.003
  18. P.E. Jupp, J.T. Kent, Fitting smooth paths to spherical data, J. R. Stat. Soc. Ser. C 36(1), 34–46 (1987).
  19. Karcher H., Riemannian center of mass and mollifier smoothing, 10.1002/cpa.3160300502
  20. E. Klassen, A. Srivastava, Geodesic between 3D closed curves using path straightening, in European Conference on Computer Vision, ed. by A. Leonardis, H. Bischof, A. Pinz (eds.), (2006), pp. 95–106.
  21. Kume A., Dryden I. L., Le H., Shape-space smoothing splines for planar landmark data, 10.1093/biomet/asm047
  22. Lazard Michel, Tits Jacques, Domaines d'injectivité de l'application exponentielle, 10.1016/0040-9383(66)90030-9
  23. J.M. Lee, Riemannian Manifolds: An Introduction to Curvature. Graduate Texts in Mathematics, vol. 176 (Springer, New York, 2007).
  24. Linnér Anders, Symmetrized curve-straightening, 10.1016/s0926-2245(02)00144-4
  25. Machado L., Silva Leite F., Krakowski K., Higher-order smoothing splines versus least squares problems on Riemannian manifolds, 10.1007/s10883-010-9080-1
  26. L. Machado, F. Silva Leite, Fitting smooth paths on Riemannian manifolds, Int. J. Appl. Math. Stat. 4(J06), 25–53 (2006).
  27. Machado Luís, Leite F. Silva, Hüper Knut, Riemannian Means as Solutions of Variational Problems, 10.1112/s1461157000001200
  28. Milnor John, Morse Theory. (AM-51), ISBN:9781400881802, 10.1515/9781400881802
  29. NOAKES LYLE, HEINZINGER GREG, PADEN BRAD, Cubic Splines on Curved Spaces, 10.1093/imamci/6.4.465
  30. B. O’Neill, Semi-Riemannian Geometry. Pure and Applied Mathematics, vol. 103 (Academic Press [Harcourt Brace Jovanovich Publishers], New York, 1983).
  31. Palais Richard S., Morse theory on Hilbert manifolds, 10.1016/0040-9383(63)90013-2
  32. Popiel Tomasz, Noakes Lyle, Bézier curves and C2 interpolation in Riemannian manifolds, 10.1016/j.jat.2007.03.002
  33. C. Samir, P.A. Absil, A. Srivastava, E. Klassen, A gradient-descent method for curve fitting on Riemannian manifolds, Tech. Rep. UCL-INMA-2009.023-v3, Université catholique de Louvain (2010).
  34. Shingel T., Interpolation in special orthogonal groups, 10.1093/imanum/drn033
  35. Smyrlis G., Zisis V., Local convergence of the steepest descent method in Hilbert spaces, 10.1016/j.jmaa.2004.06.051
  36. Tromba A. J., A general approach to Morse theory, 10.4310/jdg/1214433845
  37. Wallner J., Yazdani E. Nava, Grohs P., Smoothness Properties of Lie Group Subdivision Schemes, 10.1137/060668353
Bibliographic reference Samir, Chafik ; Absil, Pierre-Antoine ; Srivastava, A. ; Klassen, E.. A Gradient-Descent Method for Curve Fitting on Riemannian Manifolds. In: Foundations of Computational Mathematics, Vol. 12, no. 1, p. 49-73 (2012)
Permanent URL http://hdl.handle.net/2078.1/106702