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arXiv · 2605.12932

An NPDo Approach for Tensor Block-Diagonalization

Ren-Cang Li·Li Wang·Mei Yang
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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.

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Ren-Cang Li, Li Wang, Mei Yang. 2026-05-13. An NPDo Approach for Tensor Block-Diagonalization. https://arxiv.org/abs/2605.12932

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