Cholesky QR-based retraction on the generalized Stiefel manifold
Cholesky QR-based retraction on the generalized Stiefel manifold
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DOI：
10.1007/s10589-018-0046-7
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发表时间：
2019-03-01
影响因子：
2.2
通讯作者：
Aihara, Kensuke
中科院分区：
文献类型：
--
作者：
Sato, Hiroyuki;Aihara, Kensuke
当在黎曼流形上优化时，使用有效的收缩是很重要的，它将切空间上的一个点映射到流形上的一个点。本文证明了基于QR分解的映射是广义Stiefel流形上的收缩映射。此外，我们提出了一个有效的实现收缩的基础上Cholesky QR分解。数值实验表明，所提出的收缩比现有的基于极分解的收缩更有效。
When optimizing on a Riemannian manifold, it is important to use an efficient retraction, which maps a point on a tangent space to a point on the manifold. In this paper, we prove a map based on the QR factorization to be a retraction on the generalized Stiefel manifold. In addition, we propose an efficient implementation of the retraction based on the Cholesky QR factorization. Numerical experiments show that the proposed retraction is more efficient than the existing one based on the polar factorization.