{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T00:50:04Z","timestamp":1790643004953,"version":"4.1.0"},"reference-count":14,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-10-IAIHU-06"],"award-info":[{"award-number":["ANR-10-IAIHU-06"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["678304"],"award-info":[{"award-number":["678304"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["666992"],"award-info":[{"award-number":["666992"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2018,1]]},"abstract":"<jats:p>Parallel transport on Riemannian manifolds allows one to connect tangent spaces at different points in an isometric way and is therefore of importance in many contexts, such as statistics on manifolds. The existing methods for computing parallel transport require either the computation of Riemannian logarithms, such as Schild's ladder, or the Christoffel symbols. The logarithm is rarely given in closed form, and therefore expensive to compute, whereas the Christoffel symbols are in general hard and costly to compute. From an identity between parallel transport and Jacobi fields, we propose a numerical scheme to approximate parallel transport along a geodesic. We find and prove an optimal convergence rate for the scheme, which is equivalent to Schild's ladders. We investigate potential variations of the scheme and give experimental results on the Euclidean 2-sphere and on the manifold of symmetric positive definite matrices.<\/jats:p>","DOI":"10.1137\/17m1130617","type":"journal-article","created":{"date-parts":[[2018,8,9]],"date-time":"2018-08-09T10:06:44Z","timestamp":1533809204000},"page":"2563-2584","source":"Crossref","is-referenced-by-count":22,"title":["A Fanning Scheme for the Parallel Transport along Geodesics on Riemannian Manifolds"],"prefix":"10.1137","volume":"56","author":[{"given":"Maxime","family":"Louis","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Benjamin","family":"Charlier","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Paul","family":"Jusselin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Susovan","family":"Pal","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Stanley","family":"Durrleman","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2018,8,9]]},"reference":[{"key":"atypb1","volume-title":"Grad. 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Sci. 171, Springer, 2010.","DOI":"10.1007\/978-3-642-12055-8"},{"key":"atypb14","first-page":"1178","volume-title":"Advances in Neural Information Processing Systems","author":"Zhang M.","year":"2013"}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/17M1130617","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:48:57Z","timestamp":1787334537000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/17M1130617"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,1]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2018,1]]}},"alternative-id":["10.1137\/17M1130617"],"URL":"https:\/\/doi.org\/10.1137\/17m1130617","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,1]]}}}