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Matrix Anal. Appl."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>The affine Grassmannian is a noncompact smooth manifold that parameterizes all affine subspaces of a fixed dimension. It is a natural generalization of Euclidean space, points being zero-dimensional affine subspaces. We will realize the affine Grassmannian as a matrix manifold and extend Riemannian optimization algorithms including steepest descent, Newton method, and conjugate gradient, to real-valued functions on the affine Grassmannian. Like their counterparts for the Grassmannian, they rely only on standard numerical linear algebra and are readily computable.<\/jats:p>","DOI":"10.1137\/18m1169321","type":"journal-article","created":{"date-parts":[[2019,4,5]],"date-time":"2019-04-05T12:17:33Z","timestamp":1554466653000},"page":"371-393","source":"Crossref","is-referenced-by-count":10,"title":["Numerical Algorithms on the Affine Grassmannian"],"prefix":"10.1137","volume":"40","author":[{"given":"Lek-Heng","family":"Lim","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5235-560X","authenticated-orcid":true,"given":"Ken","family":"Sze-Wai Wong","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ke","family":"Ye","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,4,3]]},"reference":[{"key":"atypb1","doi-asserted-by":"crossref","unstructured":"P.A. 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