Interpolation in special orthogonal groups

IMA Journal of Numerical Analysis

Volumn 29, Issue 3, 2009, Pages 731-745

  Shingel, Tatiana ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Interpolation; Lie groups; Special orthogonal group

Indexed keywords

INTERPOLATION;

EXPONENTIAL REPRESENTATION; LIE ALGEBRA; MULTI-VALUED; PRACTICAL IMPORTANCE; SPECIAL ORTHOGONAL GROUP;

LIE GROUPS;

EID: 67651177882     PISSN: 02724979     EISSN: 14643642     Source Type: Journal    
DOI: 10.1093/imanum/drn033     Document Type: Article

References (19)

1. ADAMS, F. (1982) Lectures on Lie Groups. Chicago, IL: The University of Chicago Press.
2. BAKER JR, G. A. (1975) Essentials of Padé Approximants. New York: Academic Press.
3. BLOCH, A. M. & ISERLES, A. (2005) Commutators of skew-symmetric matrices. Int. J. Bifurcat. Chaos, 15, 793-801.
4. CROUCH, P., KUN, G. & LEITE, F. S. (1999) The De Casteljau algorithm on Lie groups and spheres. J. Dyn. Control Syst., 3, 397-429.
5. HIGHAM, N. J. (2006) Functions of matrices. Handbook of Linear Algebra (L. Hogben ed.). Boca Raton, FL: Chapman and Hall/CRC, pp. 11.1-11.13.
6. HORN, R. A. & JOHNSON, C. R. (1991) Topics in Matrix Analysis. Cambridge: Cambridge University Press.
7. n, SO(n) andGraßmann manifolds. Technical Report SISSA 56/2005/M. Trieste, Italy: International School for Advanced Studies.
8. ISERLES, A. (2001) A Magnus expansion for the equation Y′ = AY - YB. J. Comput. Math., 19, 15-26.
9. ISERLES, A., MUNTHE-KAAS, H., NøRSETT, S. P. & ZANNA, A. (2000) Lie-group methods. Acta Numer., 9, 215-365.
10. KANG, I. G. & PARK, F. C. (1999) Cubic spline algorithms for orientation interpolation. Int. J. Numer. Eng., 46, 45-64.
11. LEWIS, D. & OLVER, P. J. (2002) Geometric integration algorithms on homogeneous manifolds. Found. Comput. Math., 2, 363-392.
12. MAGNUS, W. (1954) On the exponential solution of differential equations for a linear operator. Commun. Pure Appl. Math., 7, 649-767.
13. MARTHINSEN, A. (1999) Interpolation in Lie groups. SIAMJ. Numer. Anal., 37, 269-285.
14. MOAN, P. C, OTEO, J. & ROS, J. (1999) On the existence of the exponential solution of linear differential systems. J. Phys. A Math. Gen., 32, 5133-5139.
15. OLVER, P. J. (1995) Equivalence, Invariants, and Symmetry. New York: Cambridge University Press.
16. PARK, F. & RAVANI, B. (1995) Bézier curves on Riemannian manifolds and Lie groups with kinematic applications. ASMEJ. Mech. Des., 117, 36-40.
17. PRESLEY, A. & SEGAL, G. (1986) Loop Groups. New York: Oxford University Press.
18. RODRIGUES, R. C, LEITE, F. S. & JAKUBIAK, J. (2005) A new geometric algorithm to generate smooth interpolating curves on Riemannian manifolds. LMS J. Comput. Math., 8, 251-266.
19. VARADARAJAN, V. S. (1984) Lie Groups, Lie Algebras, and Their Representations. New York: Springer.