An NPDo Approach for Tensor Block-Diagonalization
Abstract
This paper is concerned with Partial Tensor Block-Diagonalization of a multiway tensor by orthonormal matrices so that the extracted block-diagonal part optimally represents the tensor. The basic idea is to maximize the block-diagonal part via the tensor's mode-multiplications by orthonormal matrices. For that reason, it will be referred to Principal Tensor Block-Diagonalization (PTBD), which contains the Tucker decomposition (TD) of a tensor as a special case with just one block. Also as a special case is the approximate dominant tensor SVD in which each block-size is 1-by-1. An NPDo approach is proposed to optimize the block-diagonal part for computing \ptbd. It is shown the NPDo approach combined with Gauss-Seidel-type updating is globally convergent to a stationary point while the objective increases monotonically. Numerical experiments are presented to illustrate the efficiency of the NPDo approach.
Cite
@article{arxiv.2605.12932,
title = {An NPDo Approach for Tensor Block-Diagonalization},
author = {Ren-Cang Li and Li Wang and Mei Yang},
journal= {arXiv preprint arXiv:2605.12932},
year = {2026}
}
Comments
arXiv admin note: text overlap with arXiv:2605.09202