caa a22 4500 388046554 CHVBK 20180307125040.0 cr unu---uuuuu 161130e199808 xx s 000 0 eng 10.1017/S1446788700039380 doi S1446788700039380 pii (NATIONALLICENCE)cambridge-10.1017/S1446788700039380 Noakes Lyle Department of Mathematics, The University of Western Australia, Nedlands WA 6907, Australia email: lyle@maths.uwa.edu.au A Global algorithm for geodesics [Elektronische Daten] [Lyle Noakes] The problem of finding a george joinning given points x0, x1 in a connected complete Riemannian manifold requires much more effort than determining a geodesic from initial data. Boundary value problems of this type are sometimes solved using shooting methods, which work best when good initial guesses are available expectually when x0, x1 are nearby. Galerkin methods have their drawbacks too. The situation is much more difficult with general variational problems, which is why we focus on the Riemannian case. Our global algorithm is very simple to implement, and works well in practice, with no need for an initial guess. The proof of convergence to elementary and very carefully stated. with a view to possible generalizations latter on we have in mind the much larger class of interesting problems arising in optimal control especially from mechanical engineering. Copyright © Australian Mathematical Society 1998 primary 34B15 nationallicence 49M05 nationallicence secondary 53C22 nationallicence Journal of the Australian Mathematical Society Cambridge University Press 65/1(1998-08), 37-50 1446-7887 65:1<37 1998 65 JAZ https://doi.org/10.1017/S1446788700039380 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S1446788700039380 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Noakes Lyle Department of Mathematics, The University of Western Australia, Nedlands WA 6907, Australia email: lyle@maths.uwa.edu.au NATIONALLICENCE 773 0- Journal of the Australian Mathematical Society Cambridge University Press 65/1(1998-08), 37-50 1446-7887 65:1<37 1998 65 JAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge