A complex singular value decomposition algorithm based on the Riemannian Newton method
A complex singular value decomposition algorithm based on the Riemannian Newton method
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DOI：
10.1109/cdc.2013.6760335
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发表时间：
2013-12
期刊：
影响因子：
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通讯作者：
Hiroyuki Sato;T. Iwai
中科院分区：
文献类型：
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作者：
Hiroyuki Sato;T. Iwai
在本文中，求解复矩阵的奇异值分解（SVD）问题被表述为两个复 Stiefel 流形乘积的优化问题。在黎曼牛顿法的基础上，提出了一种新的复数奇异值分解算法。该算法可以提供与任意数量的奇异值相关联的奇异向量，从最大的奇异值到较小的奇异值。此外，一旦给出足够精确的近似复数 SVD，黎曼牛顿法就可以将其提高到计算机精度允许的程度。
In this paper, the problem of finding the singular value decomposition (SVD) of a complex matrix is formulated as an optimization problem on the product of two complex Stiefel manifolds. A new algorithm for the complex SVD is proposed on the basis of the Riemannian Newton method. This algorithm can provide the singular vectors associated with an arbitrary number of the singular values from the largest one down to a smaller one. Furthermore, once a sufficiently accurate approximate complex SVD is given, the Riemannian Newton method can improve it to be as accurate as the computer accuracy permits.