  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.
