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Petre Birtea - Ioan Casu (UVT): Steepest descent and Newton algorithms on orthogonal Stiefel manifolds

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Tuesday, 11. April 2017, 10:00 - 12:00
Abstract. Various well known problems (Procrustes problem, Penrose regression problem, extrema of sums of heterogeneous quadratic forms, etc.) are in fact optimization problems on Stiefel manifolds. We give a description of Newton and steepest descent algorithms on an orthogonal Stiefel manifold using only the ambient coordinates (usually Euclidean coordinates) and the geometry of such a constraint manifold. We present two different choices of a basis for the tangent space at a given point of the Stiefel manifold, that are convenient for the implementation of the numerical algorithms.
Location : Bolyai Intézet, II. emelet, Rédei terem, Aradi Vértanúk tere 1., Szeged


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