Tensor LU and QR decompositions and their randomized algorithms

Abstract

In this paper, we propose two decompositions extended from matrices to tensors, including LU and QR decompositions with their rank-revealing and randomized variations. We give the growth order analysis of error of the tensor QR (t-QR) and tensor LU (t-LU) decompositions. Growth order of error and running time are shown by numerical examples. We test our methods by compressing and analyzing the imagebased data, showing that the performance of tensor randomized QR decomposition is better than the tensor randomized SVD (t-rSVD) in terms of the accuracy, running time and memory.