Tensor LU and QR decompositions and their randomized algorithms

نویسندگان
Zhu, Yuefeng ID 1
Wei, Yimin ID 2

1 School of Mathematical Sciences, Fudan University, Shanghai, P.R. China

2 School of Mathematical Sciences and Shanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, Shanghai, PR China

doi
10.52547/CMCMA.1.1.1
چکیده

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 image-based 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.

کلیدواژه‌ها
LU decomposition, QR decomposition, rank-revealing algorithm, randomized algorithm, tensor T-product, low-rank approximation