A Riemannian gradient ascent algorithm with applications to orthogonal approximation problems of symmetric tensors

In this paper, we propose an ascent algorithm by exploiting the Riemannian gradient, which is to solve the optimization problems with orthogonality constraints. It applies to orthogonal approximation problems of symmetric tensors. The iteration possesses some nice properties and has the same express...

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Vydáno v:Applied numerical mathematics Ročník 182; s. 235 - 247
Hlavní autoři: Sheng, Zhou, Yang, Weiwei, Wen, Jie
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.12.2022
Témata:
Global convergence
Riemannian gradient
Symmetric tensor
Tensor approximation
Łojasiewicz gradient inequality
Riemannian gradient
Global convergence
Tensor approximation
Łojasiewicz gradient inequality
Symmetric tensor
ISSN:0168-9274, 1873-5460
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Shrnutí:In this paper, we propose an ascent algorithm by exploiting the Riemannian gradient, which is to solve the optimization problems with orthogonality constraints. It applies to orthogonal approximation problems of symmetric tensors. The iteration possesses some nice properties and has the same expression as the Polar decomposition. We establish that the global convergence of our algorithm. Preliminary results show that the computational advantage of our algorithm.
ISSN:0168-9274
1873-5460
DOI:10.1016/j.apnum.2022.08.005