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On matrix exponentials and their approximations related to optimization on the Stiefel manifold. (English) Zbl 07078371
Summary: In this paper we probe into the geometric properties of matrix exponentials and their approximations related to optimization on the Stiefel manifold. The relation between matrix exponentials and geodesics or retractions on the Stiefel manifold is discussed. Diagonal Padé approximation to matrix exponentials is used to construct new retractions. A Krylov subspace implementation of the new retractions is also considered for the orthogonal group and the Stiefel manifold with a very high rank.
90C Mathematical programming
Full Text: DOI
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