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Volumn 16, Issue 1, 2010, Pages 121-148

Higher-order smoothing splines versus least squares problems on Riemannian manifolds

Author keywords

Geometric polynomials; Least square problems; Lie groups; Riemannian manifolds; Smoothing splines

Indexed keywords

LEAST SQUARE PROBLEMS; LIE GROUP; RIEMANNIAN MANIFOLD; SMOOTHING SPLINE; SMOOTHING SPLINES;

EID: 75049084413     PISSN: 10792724     EISSN: 15738698     Source Type: Journal    
DOI: 10.1007/s10883-010-9080-1     Document Type: Article
Times cited : (54)

References (34)
  • 2
    • 75049085858 scopus 로고    scopus 로고
    • On mechanical systems with nonholonomic constraints and symmetries
    • F Bullo M Zefran 1998 On mechanical systems with nonholonomic constraints and symmetries Systems Control Lett. 42 1/2 135 164
    • (1998) Systems Control Lett. , vol.42 , Issue.1-2 , pp. 135-164
    • Bullo, F.1    Zefran, M.2
  • 3
    • 0003232417 scopus 로고    scopus 로고
    • Spherical averages and applications to spherical splines and interpolation
    • 10.1145/502122.502124
    • SR Buss JP Fillmore 2001 Spherical averages and applications to spherical splines and interpolation ACM Trans. Graph. 2 20 95 126 10.1145/502122.502124
    • (2001) ACM Trans. Graph. , vol.2 , Issue.20 , pp. 95-126
    • Buss, S.R.1    Fillmore, J.P.2
  • 6
    • 0001480429 scopus 로고    scopus 로고
    • On the geometry of Riemannian cubic polynomials
    • -, On the geometry of Riemannian cubic polynomials. Differ. Geom. Appl. (2001), No. 15, 107-135.
    • (2001) Differ. Geom. Appl. , vol.15 , pp. 107-135
  • 7
    • 0020909271 scopus 로고
    • Formulation and optimization of cubic polynomial joint trajectories for industrial robots
    • C Lin Chang PJ Luh 1983 Formulation and optimization of cubic polynomial joint trajectories for industrial robots IEEE Trans. Automat. Control AC28 1066 1074
    • (1983) IEEE Trans. Automat. Control , vol.28 , pp. 1066-1074
    • Lin Chang, C.1    Luh, P.J.2
  • 8
    • 0033155646 scopus 로고    scopus 로고
    • De Casteljau algorithm on Lie groups and spheres
    • DOI 10.1023/A:1021770717822
    • P Crouch G Kun F Silva Leite 1999 The De Casteljau algorithm on Lie groups and spheres J. Dynam. Control Systems 5 3 397 429 0961.53027 10.1023/A:1021770717822 1706785 (Pubitemid 32080737)
    • (1999) Journal of Dynamical and Control Systems , vol.5 , Issue.3 , pp. 397-429
    • Crouch, P.1    Kun, G.2    Silva Leite, F.3
  • 9
    • 0026400341 scopus 로고
    • Geometry and the dynamic interpolation problem
    • Boston
    • P. Crouch and F. Silva Leite, Geometry and the dynamic interpolation problem. Proc. Amer. Control Conf. Boston (1991), 1131-1137.
    • (1991) Proc. Amer. Control Conf. , pp. 1131-1137
    • Crouch, P.1    Silva Leite, F.2
  • 10
    • 0001261818 scopus 로고
    • The dynamic interpolation problem: On Riemannian manifolds, Lie groups, and symmetric spaces
    • 0946.58018 10.1007/BF02254638 1333770
    • P Crouch F Silva Leite 1995 The dynamic interpolation problem: on Riemannian manifolds, Lie groups, and symmetric spaces J. Dynam. Control Systems 1 2 177 202 0946.58018 10.1007/BF02254638 1333770
    • (1995) J. Dynam. Control Systems , vol.1 , Issue.2 , pp. 177-202
    • Crouch, P.1    Silva Leite, F.2
  • 13
    • 75049085606 scopus 로고
    • Curves and surfaces for computer aided geometric design
    • G. Farin, Curves and surfaces for computer aided geometric design. Academic Press (1990).
    • (1990) Academic Press
    • Farin, G.1
  • 14
    • 0036913308 scopus 로고    scopus 로고
    • An analytical theory for Riemannian cubic polynomials
    • 10.1093/imamci/19.4.445 1949013
    • R Giamgò F Giannoni P Piccione 2002 An analytical theory for Riemannian cubic polynomials IMA J. Math. Control Inform. 19 445 460 10.1093/imamci/19.4.445 1949013
    • (2002) IMA J. Math. Control Inform , vol.19 , pp. 445-460
    • Giamgò, R.1    Giannoni, F.2    Piccione, P.3
  • 17
    • 0001872605 scopus 로고
    • Fitting smooth paths to spherical data
    • 0613.62086 10.2307/2347843 887825
    • PE Jupp JT Kent 1987 Fitting smooth paths to spherical data Appl. Statist. 36 1 34 46 0613.62086 10.2307/2347843 887825
    • (1987) Appl. Statist. , vol.36 , Issue.1 , pp. 34-46
    • Jupp, P.E.1    Kent, J.T.2
  • 18
    • 84980162923 scopus 로고
    • Riemannian center of mass and mollifier smoothing
    • 0354.57005 10.1002/cpa.3160300502 442975
    • H Karcher 1977 Riemannian center of mass and mollifier smoothing Commun. Pure Appl. Math. 30 509 541 0354.57005 10.1002/cpa.3160300502 442975
    • (1977) Commun. Pure Appl. Math. , vol.30 , pp. 509-541
    • Karcher, H.1
  • 19
    • 22544477953 scopus 로고    scopus 로고
    • Ph.D. Thesis, Department of Mathematics and Statistics, The University of Western Australia
    • A. K. Krakowski, Geometrical methods of inference. Ph.D. Thesis, Department of Mathematics and Statistics, The University of Western Australia (2002).
    • (2002) Geometrical Methods of Inference
    • Krakowski, A.K.1
  • 22
    • 75049086135 scopus 로고    scopus 로고
    • Ph.D. Thesis, Department of Mathematics, University of Coimbra, Portugal
    • L. Machado, Least squares problems on Riemannian manifolds. Ph.D. Thesis, Department of Mathematics, University of Coimbra, Portugal (2006).
    • (2006) Least Squares Problems on Riemannian Manifolds
    • MacHado, L.1
  • 23
    • 42949153601 scopus 로고    scopus 로고
    • Riemannian means as solutions of variational problems
    • L. Machado, F. Silva Leite, and K. Hüper, Riemannian means as solutions of variational problems. LMS J. Comput. Math. (2006), No. 8, 86-103.
    • (2006) LMS J. Comput. Math. , vol.8 , pp. 86-103
    • L. Machado1
  • 24
    • 38649109729 scopus 로고    scopus 로고
    • Fitting smooth paths on Riemannian manifolds
    • 1138.65012 2262660
    • L Machado F Silva Leite 2006 Fitting smooth paths on Riemannian manifolds Int. J. Appl. Math. Statist. 4 J06 25 53 1138.65012 2262660
    • (2006) Int. J. Appl. Math. Statist. , vol.4 , Issue.J06 , pp. 25-53
    • MacHado, L.1    Silva Leite, F.2
  • 25
    • 0004190360 scopus 로고
    • Princeton University Press Princeton, New Jersey 0108.10401
    • J. W. Milnor, Morse theory. Princeton University Press, Princeton, New Jersey 1963.
    • (1963) Morse Theory
    • Milnor, J.W.1
  • 26
    • 22944439423 scopus 로고    scopus 로고
    • A differential geometric approach to the geometric mean of symmetric positive-definite matrices
    • DOI 10.1137/S0895479803436937
    • M Moakher 2005 A differential geometric approach to the arithmetic and geometric means of operators in some symmetric spaces SIAM. J. Matrix Anal. Appl. 26 3 735 747 1079.47021 10.1137/S0895479803436937 2137480 (Pubitemid 41049842)
    • (2005) SIAM Journal on Matrix Analysis and Applications , vol.26 , Issue.3 , pp. 735-747
    • Moakher, M.1
  • 27
    • 0024929710 scopus 로고
    • Cubic splines on curved spaces
    • 0698.58018 10.1093/imamci/6.4.465 1036158
    • L Noakes G Heinzinger B Paden 1989 Cubic splines on curved spaces IMA J. Math. Control Inform. 6 465 473 0698.58018 10.1093/imamci/6.4.465 1036158
    • (1989) IMA J. Math. Control Inform , vol.6 , pp. 465-473
    • Noakes, L.1    Heinzinger, G.2    Paden, B.3
  • 28
    • 0029277611 scopus 로고
    • Bézier curves on Riemannian manifolds and Lie groups with kinematic applications
    • 10.1115/1.2826114
    • F Park B Ravani 1995 Bézier curves on Riemannian manifolds and Lie groups with kinematic applications ASME J. Mech. Design 117 36 40 10.1115/1.2826114
    • (1995) ASME J. Mech. Design , vol.117 , pp. 36-40
    • Park, F.1    Ravani, B.2
  • 29
  • 30
    • 34250516079 scopus 로고
    • Smoothing by spline functions
    • 0161.36203 10.1007/BF02162161 295532
    • CH Reinsch 1967 Smoothing by spline functions Numer. Math. 10 177 183 0161.36203 10.1007/BF02162161 295532
    • (1967) Numer. Math. , vol.10 , pp. 177-183
    • Reinsch, C.H.1
  • 31
    • 0033243805 scopus 로고    scopus 로고
    • Closed forms for the exponential mapping on matrix Lie groups based on Putzer's method
    • 0942.22009 10.1063/1.532908 1696944
    • F Silva Leite P Crouch 1999 Closed forms for the exponential mapping on matrix Lie groups based on Putzer's method J. Math. Phys. 40 3561 3568 0942.22009 10.1063/1.532908 1696944
    • (1999) J. Math. Phys. , vol.40 , pp. 3561-3568
    • Silva Leite, F.1    Crouch, P.2
  • 34
    • 0032138442 scopus 로고
    • On the generation of smooth three-dimensional rigid body motions
    • M Zefran V Kumar C Croke 1995 On the generation of smooth three-dimensional rigid body motions IEEE Trans. Robotics Automat. 14 4 579 589
    • (1995) IEEE Trans. Robotics Automat. , vol.14 , Issue.4 , pp. 579-589
    • Zefran, M.1    Kumar, V.2    Croke, C.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.