Riemannian conjugate gradient method for complex singular value decomposition problem
Riemannian conjugate gradient method for complex singular value decomposition problem
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DOI：
10.1109/cdc.2014.7040305
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发表时间：
2014-12
期刊：
影响因子：
--
通讯作者：
Hiroyuki Sato
中科院分区：
文献类型：
--
作者：
Hiroyuki Sato
本文提出了一种求解与复矩阵奇异值分解有关的黎曼优化问题的黎曼共轭梯度法。该算法是全局收敛的，不同于牛顿法。然而，牛顿法对此问题是局部二次收敛的。考虑到这一点，建议的共轭梯度法结合牛顿法产生的混合算法，这是全局和二次收敛的实践。
In this paper, a Riemannian conjugate gradient method for a Riemannian optimization problem related to the singular value decomposition of a complex matrix is developed. The proposed algorithm is globally convergent, unlike Newton's method. However, Newton's method for this problem is locally quadratically convergent. With this in mind, the proposed conjugate gradient method is combined with Newton's method to produce a hybrid algorithm, which is globally and quadratically convergent in practice.