Generalized L-product for hight order tensors with applications using GPU computation

TL;DR

This paper introduces a generalized L-product for high-order tensors, extending existing tensor products like cosine and T-products, with applications in tensor completion and GPU-accelerated computation.

Contribution

It proposes a new generalized L-product for high-order tensors, extending tensor cosine and T-products, and demonstrates its effectiveness in tensor completion tasks with GPU acceleration.

Findings

Effective tensor completion using the proposed methods

Significant speedup with GPU implementation

Numerical results confirm the approach's efficiency

Abstract

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.