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134 ANTONELLA ZANNA
[15] Stein Krogstad, Hans Munthe-Kaas, and Antonella Zanna. Generalized polar coordinates on Lie groups and numerical integrators. Numerische Mathematik, 114(1):161–187, 11 2009.
[16] W. Magnus. On the Exponential Solution of Di↵erential Equations for a Linear Operator. Comm. Pure and Appl. Math., VII:649–673, 1954.
[17] H. Munthe-Kaas, R. G. W. Quispel, and A. Zanna. Generalized polar decompositions on Lie groups with involutive automorphisms. Found. Comp. Math., 1(3):297–324, 2001.
[18] Brynjulf Owren and Arne Marthinsen. Integration methods based on canonical coordinates of the second kind. Numer. Math., 87(4):763–790, 2001.
[19] K. Spindler. Motion planning via optimal control theory. In American Control Conference, 2002. Proceedings of the 2002, volume 3, pages 1972–1977. IEEE, 2002.
[20] V. S. Varadarajan. Lie Groups, Lie Algebras, and Their Representation. GTM 102. Springer- Verlag, 1984.
[21] A. Zanna and H. Z. Munthe-Kaas. Generalized polar decompositions for the approximation of the matrix exponential. SIAM J. Matrix Anal., 23(3):840–862, 2002.
[22] Antonella Zanna. Recurrence relations and convergence theory of the generalized polar de- composition on Lie groups. Math. Comp., 73(246):761–776 (electronic), 2004.
(A. Zanna) Department of Mathematics University of Bergen
Johannes Brunsgt 12
N-5020 Bergen
Norway
E-mail address: A.Zanna@math.uib.no


































































































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