高阶张量的广义L-积及其在GPU计算中的应用
Generalized L-product for hight order tensors with applications using GPU computation
摘要：
在本文中，我们将提出一个推广的L-张量积（L-产品），包括推广著名的张量余弦和T-产品，定义为三阶张量和快速傅里叶变换和离散余弦变换（DCT）的基础上。我们将给出张量完备化的一些应用。为了解决与张量完备化问题相关的一些最优化问题，我们将使用近似梯度算法（PGA）来解决一些派生的最优化问题。数值试验表明了所提出方法的有效性，并给出了一些测试使用GPU计算。
英文摘要：
In this paper, we will present a generalization of the L-tensor product (L-product) including generalization of the well known tensor cosine and T-products that were defined for third-order tensors and based on fast Fourier transform and discrete cosine transform (DCT). We will give some applications on tensor completion. To solve some optimization problems linked with the problem of tensor completion, we will use the Proximal Gradient Algorithm (PGA) to solve some derived optimization problems. Numerical tests are given to show the effectiveness of the proposed methods and also present some tests using GPU computation.
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