论文标题
Grassman基质对的广义奇异值的新公式和计算
New Formulation and Computation for Generalized Singular Values of Grassman Matrix Pair
论文作者
论文摘要
在本文中，我们得出了用于计算Grassman矩阵对的广义奇异值的新模型公式。这些新的配方利用截短的滤镜矩阵来定位Grassman矩阵对的$ i $ th概括。可以通过使用涉及牛顿在Grassmann歧管上的牛顿方法的数值方法来解决所得的矩阵优化问题。据报道，关于综合数据集和基因表达数据集的数值示例，证明了针对计算格拉曼矩阵对的任意概括性奇异值的高精度和快速计算。
In this paper, we derive new model formulations for computing generalized singular values of a Grassman matrix pair. These new formulations make use of truncated filter matrices to locate the $i$-th generalized singular value of a Grassman matrix pair. The resulting matrix optimization problems can be solved by using numerical methods involving Newton's method on Grassmann manifold. Numerical examples on synthetic data sets and gene expression data sets are reported to demonstrate the high accuracy and the fast computation of the proposed new ormulations for computing arbitrary generalized singular value of Grassman matrix pair.
